Factors

Excerpts

Factors
The factors of a monomial may be found by inspection. Thus, the factors of $21a^{2}b$ are $3$, $7$, $a$, $a$, and $b$.
Factors
Take the square root of the first term and the square root of the second term. The sum of these roots will form the first factor; The difference of these roots will form the second factor.
Factors
The first two terms of $ac + ad + bc + bd$ are seen to have the common factor $a$, and the last two terms, the common factor $b$. Hence we bracket the first two terms and also the last two terms.
Factors
Here the last two terms, $-bc - bd$, being put within a parenthesis preceded by the sign $-$, have their signs changed to $+$.
Factors
Since the product is $+12$, the two numbers are *both positive* or *both negative*, and since their sum is $-7$, they must both be negative.
Factors
In like manner we can resolve into factors any expression which can be written as the difference of two cubes.

Equations

Factors
3a^{2} - 6ab &= 3a(a - 2b)
A polynomial whose terms share the factor 3a is resolved by taking 3a out as a factor.
Factors
4x^{3} + 12x^{2} - 8x &= 4x(x^{2} + 3x - 2)
The common factor 4x is taken out of each term of the polynomial, leaving the quotient in brackets.
Factors
(x + y)(x - y) = x^{2} - y^{2}
The product of the sum and the difference of two quantities equals the difference of their squares, so a difference of squares factors into a sum and a difference.
This equation is in Multiplication and Division (Multiplication and Division)
Factors
a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})
The difference of two cubes is the difference of their cube roots times the sum of the squares of the roots and their product.
This equation is in Multiplication and Division (Multiplication and Division)
Factors
a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})
The sum of two cubes is the sum of their cube roots times the square of the first root, minus their product, plus the square of the second root.
Factors
(x + y)^{2} = x^{2} + 2xy + y^{2}
The square of a sum of two quantities is the square of the first, plus twice their product, plus the square of the second.
Factors
(x - y)^{2} = x^{2} - 2xy + y^{2}
The square of a difference of two quantities is the square of the first, minus twice their product, plus the square of the second.

Problems

Exercise 31

Exercise 31, problem 1, p. 72
$2x^{2} - 4x$.
Printed answer:
- $2x(x - 2)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 2*x*(x - 2)
Exercise 31, problem 10, p. 72
$3x^{3}y^{3} - 6x^{4}y^{4} - 9x^{2}y^{2}$.
Printed answer:
- $3x^{2}y^{2}(xy - 2x^{2}y^{2} - 3)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 3*x**2*y**2*(x*y - 2*x**2*y**2 - 3)
Exercise 31, problem 2, p. 72
$3a^{3} - 6a$.
Printed answer:
- $3a(a^{2} - 2)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 3*a*(a**2 - 2)
Exercise 31, problem 3, p. 72
$5a^{2}b^{2} - 10a^{3}b^{3}$.
Printed answer:
- $5a^{2}b^{2}(1 - 2ab)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 5*a**2*b**2*(1 - 2*a*b)
Exercise 31, problem 4, p. 72
$3x^{2}y + 4xy^{2}$.
Printed answer:
- $xy(3x + 4y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes x*y*(3*x + 4*y)
Exercise 31, problem 5, p. 72
$8a^{3}b^{2} + 4a^{2}b^{3}$.
Printed answer:
- $4a^{2}b^{2}(2a + b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 4*a**2*b**2*(2*a + b)
Exercise 31, problem 6, p. 72
$3a^{4} - 12a^{2} - 6a^{3}$.
Printed answer:
- $3a^{2}(a^{2} - 4 - 2a)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 3*a**2*(a**2 - 4 - 2*a)
Exercise 31, problem 7, p. 72
$4x^{2} - 8x^{4} - 12x^{5}$.
Printed answer:
- $4x^{2}(1 - 2x^{2} - 3x^{3})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 4*x**2*(1 - 2*x**2 - 3*x**3)
Exercise 31, problem 8, p. 72
$5 - 10x^{2}y^{2} + 15x^{2}y$.
Printed answer:
- $5(1 - 2x^{2}y^{2} + 3x^{2}y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 5*(1 - 2*x**2*y**2 + 3*x**2*y)
Exercise 31, problem 9, p. 72
$7a^{2} + 14a - 21a^{3}$.
Printed answer:
- $7a(a + 2 - 3a^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes 7*a*(a + 2 - 3*a**2)

Exercise 32

Exercise 32, problem 1, p. 73
$x^{3} + x^{2} + x + 1$.
Printed answer:
- $(x^{2} + 1)(x + 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x**2 + 1)*(x + 1)
Exercise 32, problem 10, p. 73
$abxy + cxy + abc + c^{2}$.
Printed answer:
- $(xy + c)(ab + c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x*y + c)*(a*b + c)
Exercise 32, problem 11, p. 73
$ax - ay - bx + cy - cx + by$.
Printed answer:
- $(a - b - c)(x - y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - b - c)*(x - y)
Exercise 32, problem 12, p. 73
$(a - b)^{2} - 2c(a - b)$.
Printed answer:
- $(a - b - 2c)(a - b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - b - 2*c)*(a - b)
Exercise 32, problem 2, p. 73
$x^{3} - x^{2} + x - 1$.
Printed answer:
- $(x^{2} + 1)(x - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x**2 + 1)*(x - 1)
Exercise 32, problem 3, p. 73
$x^{2} + xy + xz + yz$.
Printed answer:
- $(x + y)(x + z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + y)*(x + z)
Exercise 32, problem 4, p. 73
$ax - bx - ay + by$.
Printed answer:
- $(x - y)(a - b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - y)*(a - b)
Exercise 32, problem 5, p. 73
$a^{2} - ac + ab - bc$.
Printed answer:
- $(a + b)(a - c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + b)*(a - c)
Exercise 32, problem 6, p. 73
$x^{2} - bx + 3x - 3b$.
Printed answer:
- $(x + 3)(x - b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 3)*(x - b)
Exercise 32, problem 7, p. 73
$2x^{3} - x^{2} + 4x - 2$.
Printed answer:
- $(x^{2} + 2)(2x - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x**2 + 2)*(2*x - 1)
Exercise 32, problem 8, p. 73
$a^{2} - 3a - ab + 3b$.
Printed answer:
- $(a - b)(a - 3)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - b)*(a - 3)
Exercise 32, problem 9, p. 73
$6a^{2} + 2ab - 3ac - bc$.
Printed answer:
- $(2a - c)(3a + b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a - c)*(3*a + b)

Exercise 33

Exercise 33, problem 1, p. 74
$4 - x^{2}$.
Printed answer:
- $(2 + x)(2 - x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2 + x)*(2 - x)
Exercise 33, problem 10, p. 74
$81x^{2}y^{2} - 1$.
Printed answer:
- $(9xy + 1)(9xy - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (9*x*y + 1)*(9*x*y - 1)
Exercise 33, problem 11, p. 74
$49a^{2}b^{2} - 4$.
Printed answer:
- $(7ab + 2)(7ab - 2)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (7*a*b + 2)*(7*a*b - 2)
Exercise 33, problem 12, p. 74
$25a^{4}b^{4} - 9$.
Printed answer:
- $(5a^{2}b^{2} + 3)(5a^{2}b^{2} - 3)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (5*a**2*b**2 + 3)*(5*a**2*b**2 - 3)
Exercise 33, problem 13, p. 74
$9a^{8}b^{6} - 16x^{10}$.
Printed answer:
- $(3a^{4}b^{3} + 4x^{5})(3a^{4}b^{3} - 4x^{5})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*a**4*b**3 + 4*x**5)*(3*a**4*b**3 - 4*x**5)
Exercise 33, problem 14, p. 74
$144x^{2}y^{2} - 1$.
Printed answer:
- $(12xy + 1)(12xy - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (12*x*y + 1)*(12*x*y - 1)
Exercise 33, problem 15, p. 74
$100x^{6}y^{2}z^{4} - 1$.
Printed answer:
- $(10x^{3}yz^{2} + 1)(10x^{3}yz^{2} - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (10*x**3*y*z**2 + 1)*(10*x**3*y*z**2 - 1)
Exercise 33, problem 16, p. 74
$1 - 121a^{4}b^{8}c^{12}$.
Printed answer:
- $(1 + 11a^{2}b^{4}c^{6})(1 - 11a^{2}b^{4}c^{6})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (1 + 11*a**2*b**4*c**6)*(1 - 11*a**2*b**4*c**6)
Exercise 33, problem 17, p. 74
$25a^{2} - 64x^{6}y^{6}$.
Printed answer:
- $(5a + 8x^{3}y^{3})(5a - 8x^{3}y^{3})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (5*a + 8*x**3*y**3)*(5*a - 8*x**3*y**3)
Exercise 33, problem 18, p. 74
$16x^{16}-25y^{18}$.
Printed answer:
- $(4x^{8} + 5y^{9})(4x^{8} - 5y^{9})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*x**8 + 5*y**9)*(4*x**8 - 5*y**9)
Exercise 33, problem 19, p. 74
$(375)^{2} - (225)^{2}$.
Printed answer:
- $90,000$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 90000
Exercise 33, problem 2, p. 74
$9 - x^{2}$.
Printed answer:
- $(3 + x)(3 - x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3 + x)*(3 - x)
Exercise 33, problem 20, p. 74
$(579)^{2} - (559)^{2}$.
Printed answer:
- $22,760$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 22760
Exercise 33, problem 21, p. 74
$(873)^{2} - (173)^{2}$.
Printed answer:
- $732,200$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 732200
Exercise 33, problem 22, p. 74
$(101)^{2} - (99)^{2}$.
Printed answer:
- $400$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 400
On the STU-32 (STU, rpn):
```
101 ENTER 99 −
```
```
101 ENTER 99 +
```
```
×
```
Calculator: +400E+0; the book prints 400. Run on the calculator core at firmware 628c96c.
Exercise 33, problem 23, p. 74
$(7244)^{2} - (7242)^{2}$.
Printed answer:
- $28,972$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 28972
Exercise 33, problem 24, p. 74
$(3781)^{2} - (219)^{2}$.
Printed answer:
- $14,248,000$.
verified: the printed answer passed a computed check
How it was checked
- evaluate: passes 14248000
Exercise 33, problem 3, p. 74
$9a^{2} - x^{2}$.
Printed answer:
- $(3a + x)(3a - x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*a + x)*(3*a - x)
Exercise 33, problem 4, p. 74
$25 - x^{2}$.
Printed answer:
- $(5 + x)(5 - x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (5 + x)*(5 - x)
Exercise 33, problem 5, p. 74
$25x^{2} - a^{2}$.
Printed answer:
- $(5x + a)(5x - a)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (5*x + a)*(5*x - a)
Exercise 33, problem 6, p. 74
$16a^{4} - 121$.
Printed answer:
- $(4a^{2} + 11)(4a^{2} - 11)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*a**2 + 11)*(4*a**2 - 11)
Exercise 33, problem 7, p. 74
$121a^{4} - 16$.
Printed answer:
- $(11a^{2} + 4)(11a^{2} - 4)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (11*a**2 + 4)*(11*a**2 - 4)
Exercise 33, problem 8, p. 74
$4a^{2}b^{2} - c^{2}d^{2}$.
Printed answer:
- $(2ab + cd)(2ab - cd)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a*b + c*d)*(2*a*b - c*d)
Exercise 33, problem 9, p. 74
$1 - x^{2}y^{2}$.
Printed answer:
- $(1 + xy)(1 - xy)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (1 + x*y)*(1 - x*y)

Exercise 34

Exercise 34, problem 1, p. 75
$(x + y)^{2} - z^{2}$.
Printed answer:
- $(x + y + z)(x + y - z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + y + z)*(x + y - z)
Exercise 34, problem 10, p. 75
$(2a + 5c)^{2} - 1$.
Printed answer:
- $(2a + 5c + 1)(2a + 5c - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a + 5*c + 1)*(2*a + 5*c - 1)
Exercise 34, problem 11, p. 75
$1 - (2a - 5c)^{2}$.
Printed answer:
- $(1 + 2a - 5c)(1 - 2a + 5c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (1 + 2*a - 5*c)*(1 - 2*a + 5*c)
Exercise 34, problem 12, p. 75
$(a + 3b)^{2} - 16c^{2}$.
Printed answer:
- $(a + 3b + 4c)(a + 3b - 4c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 3*b + 4*c)*(a + 3*b - 4*c)
Exercise 34, problem 13, p. 75
$(a - 5b)^{2} - 9c^{2}$.
Printed answer:
- $(a - 5b + 3c)(a - 5b - 3c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 5*b + 3*c)*(a - 5*b - 3*c)
Exercise 34, problem 14, p. 75
$16c^{2} - (a - 5b)^{2}$.
Printed answer:
- $(4c + a - 5b)(4c - a + 5b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*c + a - 5*b)*(4*c - a + 5*b)
Exercise 34, problem 15, p. 75
$4a^{2} - (x + y)^{2}$.
Printed answer:
- $(2a + x + y)(2a - x - y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a + x + y)*(2*a - x - y)
Exercise 34, problem 16, p. 75
$b^{2} - (a - 2x)^{2}$.
Printed answer:
- $(b + a - 2x)(b - a + 2x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (b + a - 2*x)*(b - a + 2*x)
Exercise 34, problem 17, p. 75
$4z^{2} - (x + 3y)^{2}$.
Printed answer:
- $(2z + x + 3y)(2z - x - 3y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*z + x + 3*y)*(2*z - x - 3*y)
Exercise 34, problem 18, p. 75
$9 - (3a - 7b)^{2}$.
Printed answer:
- $(3 + 3a - 7b)(3 - 3a + 7b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3 + 3*a - 7*b)*(3 - 3*a + 7*b)
Exercise 34, problem 19, p. 75
$16a^{2} - (2b + 5c)^{2}$.
Printed answer:
- $(4a + 2b + 5c)(4a - 2b - 5c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*a + 2*b + 5*c)*(4*a - 2*b - 5*c)
Exercise 34, problem 2, p. 75
$(x - y)^{2} - z^{2}$.
Printed answer:
- $(x - y + z)(x - y - z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - y + z)*(x - y - z)
Exercise 34, problem 20, p. 75
$25c^{2} - (3a - 2x)^{2}$.
Printed answer:
- $(5c + 3a - 2x)(4c - 3a + 2x)$.
unverified: no computed check settled this one (yet)
How it was checked
- factor: the printed answer does not match the problem (5*c + 3*a - 2*x)*(4*c - 3*a + 2*x)
Exercise 34, problem 21, p. 75
$9a^{2} - (3b - 5c)^{2}$.
Printed answer:
- $(3a + 3b -5c)(3a - 3b + 5c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*a + 3*b - 5*c)*(3*a - 3*b + 5*c)
Exercise 34, problem 22, p. 75
$16y^{2} - (a - 3c)^{2}$.
Printed answer:
- $(4y + a - 3c)(4y - a + 3c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*y + a - 3*c)*(4*y - a + 3*c)
Exercise 34, problem 23, p. 75
$49m^{2} - (p + 2q)^{2}$.
Printed answer:
- $(7m + p + 2q)(7m - p - 2q)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (7*m + p + 2*q)*(7*m - p - 2*q)
Exercise 34, problem 24, p. 75
$36n^{2} - (d - 2c)^{2}$.
Printed answer:
- $(6n + d - 2c)(6n - d + 2c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (6*n + d - 2*c)*(6*n - d + 2*c)
Exercise 34, problem 25, p. 75
$(x + y)^{2} - (a + b)^{2}$.
Printed answer:
- $(x + y + a + b)(x + y - a - b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + y + a + b)*(x + y - a - b)
Exercise 34, problem 26, p. 75
$(x - y)^{2} - (a - b)^{2}$.
Printed answer:
- $(x - y + a - b)(x - y - a + b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - y + a - b)*(x - y - a + b)
Exercise 34, problem 27, p. 75
$(2x + 3)^{2} - (2a + b)^{2}$.
Printed answer:
- $(2x + 3 + 2a + b)(2x + 3 - 2a - b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x + 3 + 2*a + b)*(2*x + 3 - 2*a - b)
Exercise 34, problem 28, p. 75
$(b - c)^{2} - (a - 2x)^{2}$.
Printed answer:
- $(b - c + a - 2x)(b - c - a + 2x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (b - c + a - 2*x)*(b - c - a + 2*x)
Exercise 34, problem 29, p. 75
$(3x - y)^{2} - (2a - b)^{2}$.
Printed answer:
- $(3x - y + 2a - b)(3x - y - 2a + b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*x - y + 2*a - b)*(3*x - y - 2*a + b)
Exercise 34, problem 3, p. 75
$z^{2} - (x + y)^{2}$.
Printed answer:
- $(z + x + y)(z - x - y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (z + x + y)*(z - x - y)
Exercise 34, problem 30, p. 75
$(x - 3y)^{2} - (a + 2b)^{2}$.
Printed answer:
- $(x - 3y + a + 2b)(x - 3y - a - 2b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3*y + a + 2*b)*(x - 3*y - a - 2*b)
Exercise 34, problem 31, p. 75
$(x + 2y)^{2} - (a + 3b)^{2}$.
Printed answer:
- $(x + 2y + a + 3b)(x + 2y - a - 3b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 2*y + a + 3*b)*(x + 2*y - a - 3*b)
Exercise 34, problem 32, p. 75
$(x + y)^{2} - (a - z)^{2}$.
Printed answer:
- $(x + y + a - z)(x + y - a + z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + y + a - z)*(x + y - a + z)
Exercise 34, problem 4, p. 75
$z^{2} - (x - y)^{2}$.
Printed answer:
- $(z + x - y)(z - x + y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (z + x - y)*(z - x + y)
Exercise 34, problem 5, p. 75
$(x + y)^{2} - 4z^{2}$.
Printed answer:
- $(x + y + 2z)(x + y - 2z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + y + 2*z)*(x + y - 2*z)
Exercise 34, problem 6, p. 75
$4z^{2} - (x - y)^{2}$.
Printed answer:
- $(2z + x - y)(2z - x + y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*z + x - y)*(2*z - x + y)
Exercise 34, problem 7, p. 75
$(a + 2b)^{2} - c^{2}$.
Printed answer:
- $(a + 2b + c)(a + 2b - c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 2*b + c)*(a + 2*b - c)
Exercise 34, problem 8, p. 75
$(a - 2b)^{2} - c^{2}$.
Printed answer:
- $(a - 2b + c)(a - 2b - c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 2*b + c)*(a - 2*b - c)
Exercise 34, problem 9, p. 75
$c^{2} - (a - 2b)^{2}$.
Printed answer:
- $(c + a - 2b)(c - a + 2b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (c + a - 2*b)*(c - a + 2*b)

Exercise 35

Exercise 35, problem 1, p. 77
$8x^{3} - y^{3}$.
Printed answer:
- $(2x - y)(4x^{2} + 2xy + y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x - y)*(4*x**2 + 2*x*y + y**2)
Exercise 35, problem 10, p. 77
$64x^{3} - y^{9}$.
Printed answer:
- $(4x - y^{3})(16x^{2} + 4xy^{3} + y^{6})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*x - y**3)*(16*x**2 + 4*x*y**3 + y**6)
Exercise 35, problem 11, p. 77
$27a^{3} - 64c^{6}$.
Printed answer:
- $(3a - 4c^{2})(9a^{2} + 12ac^{2} + 16c^{4})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*a - 4*c**2)*(9*a**2 + 12*a*c**2 + 16*c**4)
Exercise 35, problem 12, p. 77
$x^{3}y^{3} - 216z^{3}$.
Printed answer:
- $(xy - 6z)(x^{2}y^{2} + 6xyz + 36z^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x*y - 6*z)*(x**2*y**2 + 6*x*y*z + 36*z**2)
Exercise 35, problem 13, p. 77
$64x^{3} - 729y^{3}$.
Printed answer:
- $(4x - 9y)(16x^{2} + 36xy + 81y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*x - 9*y)*(16*x**2 + 36*x*y + 81*y**2)
Exercise 35, problem 14, p. 77
$27a^{3} - 512c^{3}$.
Printed answer:
- $(3a - 8c)(9a^{2} + 24ac + 64c^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*a - 8*c)*(9*a**2 + 24*a*c + 64*c**2)
Exercise 35, problem 15, p. 77
$8x^{6} - 125y^{3}$.
Printed answer:
- $(2x^{2} - 5y)(4x^{4} + 10x^{2}y + 25y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x**2 - 5*y)*(4*x**4 + 10*x**2*y + 25*y**2)
Exercise 35, problem 16, p. 77
$64x^{12} - 27y^{15}$.
Printed answer:
- $(4x^{2} - 3y^{5})(16x^{8} + 12x^{4}y^{5} + 9y^{10})$.
unverified: no computed check settled this one (yet)
How it was checked
- factor: the printed answer does not match the problem (4*x**2 - 3*y**5)*(16*x**8 + 12*x**4*y**5 + 9*y**10)
Exercise 35, problem 17, p. 77
$216 - 8a^{3}$.
Printed answer:
- $(6 - 2a)(36 + 12a + 4a^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (6 - 2*a)*(36 + 12*a + 4*a**2)
Exercise 35, problem 18, p. 77
$343 - 27y^{3}$.
Printed answer:
- $(7 - 3y)(49 + 21y + 9y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (7 - 3*y)*(49 + 21*y + 9*y**2)
Exercise 35, problem 2, p. 77
$x^{3} - 1$.
Printed answer:
- $(x - 1)(x^{2} + x + 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 1)*(x**2 + x + 1)
Exercise 35, problem 3, p. 77
$x^{3}y^{3} - z^{3}$.
Printed answer:
- $(xy - z)(x^{2}y^{2} + xyz + z^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x*y - z)*(x**2*y**2 + x*y*z + z**2)
Exercise 35, problem 4, p. 77
$x^{3} - 64$.
Printed answer:
- $(x - 4)(x^{2} + 4x + 16)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 4)*(x**2 + 4*x + 16)
Exercise 35, problem 5, p. 77
$125a^{3} - b^{3}$.
Printed answer:
- $(5a - b)(25a^{2} + 5ab + b^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (5*a - b)*(25*a**2 + 5*a*b + b**2)
Exercise 35, problem 6, p. 77
$a^{3} - 343$.
Printed answer:
- $(a - 7)(a^{2} + 7a + 49)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 7)*(a**2 + 7*a + 49)
Exercise 35, problem 7, p. 77
$a^{3}b^{3} - 27c^{3}$.
Printed answer:
- $(ab - 3c)(a^{2}b^{2} + 3abc + 9c^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a*b - 3*c)*(a**2*b**2 + 3*a*b*c + 9*c**2)
Exercise 35, problem 8, p. 77
$x^{3}y^{3}z^{3} - 8$.
Printed answer:
- $(xyz - 2)(x^{2}y^{2}z^{2} + 2xyz + 4)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x*y*z - 2)*(x**2*y**2*z**2 + 2*x*y*z + 4)
Exercise 35, problem 9, p. 77
$8a^{3}b^{3} - 27y^{6}$.
Printed answer:
- $(2ab - 3y^{2})(4a^{2}b^{2} + 6aby^{2} + 9y^{4})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a*b - 3*y**2)*(4*a**2*b**2 + 6*a*b*y**2 + 9*y**4)

Exercise 36

Exercise 36, problem 1, p. 78
$x^{3} + 1$.
Printed answer:
- $(x + 1)(a^{2} - x + 1)$.
unverified: no computed check settled this one (yet)
How it was checked
- factor: the printed answer does not match the problem (x + 1)*(a**2 - x + 1)
Exercise 36, problem 10, p. 78
$y^{9} + 64x^{3}$.
Printed answer:
- $(y^{3} + 4x)(y^{6} - 4y^{3}x + 16x^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (y**3 + 4*x)*(y**6 - 4*y**3*x + 16*x**2)
Exercise 36, problem 11, p. 78
$a^{3}b^{3} + 27x^{3}$.
Printed answer:
- $(ab + 3x)(a^{2}b^{2} - 3abx + 9x^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a*b + 3*x)*(a**2*b**2 - 3*a*b*x + 9*x**2)
Exercise 36, problem 12, p. 78
$8y^{3}z^{3} + x^{6}$.
Printed answer:
- $(2yz + x^{2})(4y^{2}z^{2} - 2yzx^{2} + x^{4})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*y*z + x**2)*(4*y**2*z**2 - 2*y*z*x**2 + x**4)
Exercise 36, problem 13, p. 78
$y^{9} + 64x^{6}$.
Printed answer:
- $(y^{3} + 4x^{2})(y^{6} - 4y^{3}x^{2} + 16x^{4})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (y**3 + 4*x**2)*(y**6 - 4*y**3*x**2 + 16*x**4)
Exercise 36, problem 14, p. 78
$64a^{12} + x^{15}$.
Printed answer:
- $(4a^{4} + x^{5})(16a^{8} - 4a^{4}x^{5} + x^{10})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*a**4 + x**5)*(16*a**8 - 4*a**4*x**5 + x**10)
Exercise 36, problem 15, p. 78
$27x^{15} + 8a^{6}$.
Printed answer:
- $(3x^{5} + 2a^{2})(9x^{10} - 6x^{5}a^{2} + 4a^{4})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*x**5 + 2*a**2)*(9*x**10 - 6*x**5*a**2 + 4*a**4)
Exercise 36, problem 16, p. 78
$27x^{9} + 512$.
Printed answer:
- $(3x^{3} + 8)(9x^{6} - 24x^{3} + 64)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*x**3 + 8)*(9*x**6 - 24*x**3 + 64)
Exercise 36, problem 17, p. 78
$343 + 64x^{3}$.
Printed answer:
- $(7 + 4x)(49 - 28x + 16x^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (7 + 4*x)*(49 - 28*x + 16*x**2)
Exercise 36, problem 18, p. 78
$125 + 27y^{3}$.
Printed answer:
- $(5 + 3y)(25 - 15y + 9y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (5 + 3*y)*(25 - 15*y + 9*y**2)
Exercise 36, problem 2, p. 78
$8x^{3} + y^{3}$.
Printed answer:
- $(2x + y)(4x^{2} - 2xy + y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x + y)*(4*x**2 - 2*x*y + y**2)
Exercise 36, problem 3, p. 78
$x^{3} + 125$.
Printed answer:
- $(x + 5)(x^{2} - 5x + 25)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 5)*(x**2 - 5*x + 25)
Exercise 36, problem 4, p. 78
$64a^{3} + 27$.
Printed answer:
- $(4a + 3)(16a^{2} - 12a + 9)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*a + 3)*(16*a**2 - 12*a + 9)
Exercise 36, problem 5, p. 78
$x^{3}y^{3} + z^{3}$.
Printed answer:
- $(xy + z)(x^{2}y^{2} - xyz + z^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x*y + z)*(x**2*y**2 - x*y*z + z**2)
Exercise 36, problem 6, p. 78
$a^{3} + 64$.
Printed answer:
- $(a + 4)(a^{2} - 4a + 16)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 4)*(a**2 - 4*a + 16)
Exercise 36, problem 7, p. 78
$8a^{6} + b^{3}$.
Printed answer:
- $(2a^{2} + b)(4a^{4} - 2a^{2}b + b^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a**2 + b)*(4*a**4 - 2*a**2*b + b**2)
Exercise 36, problem 8, p. 78
$x^{3} + 343$.
Printed answer:
- $(x + 7)(x^{2} - 7x + 49)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 7)*(x**2 - 7*x + 49)
Exercise 36, problem 9, p. 78
$8 + x^{3}y^{3}z^{3}$.
Printed answer:
- $(2 + xyz)(4 - 2xyz + x^{2}y^{2}z^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2 + x*y*z)*(4 - 2*x*y*z + x**2*y**2*z**2)

Exercise 37

Exercise 37, problem 1, p. 80
$4x^{2} + 4xy + y^{2}$.
Printed answer:
- $(2x + y)(2x + y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x + y)*(2*x + y)
Exercise 37, problem 10, p. 80
$9a^{2} - 24ab + 16b^{2}$.
Printed answer:
- $(3a - 4b)(3a - 4b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (3*a - 4*b)*(3*a - 4*b)
Exercise 37, problem 11, p. 80
$x^{2} + 8xy + 16y^{2}$.
Printed answer:
- $(x + 4y)(x + 4y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 4*y)*(x + 4*y)
Exercise 37, problem 12, p. 80
$x^{2} - 8xy + 16y^{2}$.
Printed answer:
- $(x - 4y)(x - 4y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 4*y)*(x - 4*y)
Exercise 37, problem 13, p. 80
$4x^{2} - 20xy + 25y^{2}$.
Printed answer:
- $(2x - 5y)(2x - 5y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x - 5*y)*(2*x - 5*y)
Exercise 37, problem 14, p. 80
$1 + 20a + 100a^{2}$.
Printed answer:
- $(1 + 10a)(1 + 10a)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (1 + 10*a)*(1 + 10*a)
Exercise 37, problem 15, p. 80
$49a^{2} - 28a + 4$.
Printed answer:
- $(7a - 2)(7a - 2)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (7*a - 2)*(7*a - 2)
Exercise 37, problem 16, p. 80
$36a^{2} + 60ab + 25b^{2}$.
Printed answer:
- $(6a + 5b)(6a + 5b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (6*a + 5*b)*(6*a + 5*b)
Exercise 37, problem 17, p. 80
$81x^{2} - 36bx + 4b^{2}$.
Printed answer:
- $(9x - 2b)(9x - 2b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (9*x - 2*b)*(9*x - 2*b)
Exercise 37, problem 18, p. 80
$m^{2}n^{2} + 14mnx^{2} + 49x^{2}$.
Printed answer:
- $(mn + 7x^{2})(mn + 7x^{2})$.
unverified: no computed check settled this one (yet)
How it was checked
- factor: the printed answer does not match the problem (m*n + 7*x**2)*(m*n + 7*x**2)
Exercise 37, problem 2, p. 80
$x^{2} + 6xy + 9y^{2}$.
Printed answer:
- $(x + 3y)(x + 3y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 3*y)*(x + 3*y)
Exercise 37, problem 3, p. 80
$x^{2} + 16x + 64$.
Printed answer:
- $(x + 8)(x + 8)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 8)*(x + 8)
Exercise 37, problem 4, p. 80
$x^{2} + 10ax + 25a^{2}$.
Printed answer:
- $(x + 5a)(x + 5a)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 5*a)*(x + 5*a)
Exercise 37, problem 5, p. 80
$a^{2} - 16a + 64$.
Printed answer:
- $(a - 8)(a - 8)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 8)*(a - 8)
Exercise 37, problem 6, p. 80
$a^{2} - 10ab + 25b^{2}$.
Printed answer:
- $(a - 5b)(a - 5b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 5*b)*(a - 5*b)
Exercise 37, problem 7, p. 80
$c^{2} - 6cd + 9d^{2}$.
Printed answer:
- $(c - 3d)(c - 3d)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (c - 3*d)*(c - 3*d)
Exercise 37, problem 8, p. 80
$4x^{2} - 4x + 1$.
Printed answer:
- $(2x - 1)(2x - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x - 1)*(2*x - 1)
Exercise 37, problem 9, p. 80
$4a^{2} - 12ab + 9b^{2}$.
Printed answer:
- $(2a - 3b)(2a - 3b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a - 3*b)*(2*a - 3*b)

Exercise 38

Exercise 38, problem 1, p. 82
$a^{2} + 5a + 6$.
Printed answer:
- $(a + 2)(a + 3)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 2)*(a + 3)
Exercise 38, problem 10, p. 82
$c^{2} - 3c - 18$.
Printed answer:
- $(c + 3)(c - 6)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (c + 3)*(c - 6)
Exercise 38, problem 11, p. 82
$x^{2} + 9x + 14$.
Printed answer:
- $(x + 2)(x + 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 2)*(x + 7)
Exercise 38, problem 12, p. 82
$x^{2} - 9x + 14$.
Printed answer:
- $(x - 2)(x - 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 2)*(x - 7)
Exercise 38, problem 13, p. 82
$x^{2} - 5x - 14$.
Printed answer:
- $(x + 2)(x - 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 2)*(x - 7)
Exercise 38, problem 14, p. 82
$x^{2} - 9x + 20$.
Printed answer:
- $(x - 4)(x - 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 4)*(x - 5)
Exercise 38, problem 15, p. 82
$x^{2} - x - 20$.
Printed answer:
- $(x + 4)(x - 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 4)*(x - 5)
Exercise 38, problem 16, p. 82
$x^{2} + x - 20$.
Printed answer:
- $(x - 4)(x + 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 4)*(x + 5)
Exercise 38, problem 17, p. 82
$x^{2} - 10x + 21$.
Printed answer:
- $(x - 3)(x - 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3)*(x - 7)
Exercise 38, problem 18, p. 82
$x^{2} - 4x - 21$.
Printed answer:
- $(x + 3)(x - 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 3)*(x - 7)
Exercise 38, problem 19, p. 82
$x^{2} + 4x - 21$.
Printed answer:
- $(x - 3)(x + 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3)*(x + 7)
Exercise 38, problem 2, p. 82
$a^{2} - 5a + 6$.
Printed answer:
- $(a - 2)(a - 3)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 2)*(a - 3)
Exercise 38, problem 20, p. 82
$x^{2} - 15x + 56$.
Printed answer:
- $(x - 7)(x - 8)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 7)*(x - 8)
Exercise 38, problem 21, p. 82
$x^{2} - x - 56$.
Printed answer:
- $(x + 7)(x - 8)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 7)*(x - 8)
Exercise 38, problem 22, p. 82
$x^{2} - 10x + 9$.
Printed answer:
- $(x - 1)(x - 9)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 1)*(x - 9)
Exercise 38, problem 23, p. 82
$x^{2} + 13x + 30$.
Printed answer:
- $(x + 3)(x + 10)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 3)*(x + 10)
Exercise 38, problem 24, p. 82
$x^{2} + 7x - 30$.
Printed answer:
- $(x - 3)(x + 10)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3)*(x + 10)
Exercise 38, problem 25, p. 82
$x^{2} - 7x - 30$.
Printed answer:
- $(x + 3)(x - 10)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 3)*(x - 10)
Exercise 38, problem 26, p. 82
$a^{2} + ab - 6b^{2}$.
Printed answer:
- $(a - 2b)(a + 3b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 2*b)*(a + 3*b)
Exercise 38, problem 27, p. 82
$a^{2} - ab - 6b^{2}$.
Printed answer:
- $(a + 2b)(a - 3b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 2*b)*(a - 3*b)
Exercise 38, problem 28, p. 82
$a^{2} + 3ab - 4b^{2}$.
Printed answer:
- $(a - b)(a + 4b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - b)*(a + 4*b)
Exercise 38, problem 29, p. 82
$a^{2} - 3ab - 4b^{2}$.
Printed answer:
- $(a + b)(a - 4b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + b)*(a - 4*b)
Exercise 38, problem 3, p. 82
$a^{2} + 6a + 5$.
Printed answer:
- $(a + 1)(a + 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 1)*(a + 5)
Exercise 38, problem 30, p. 82
$a^{2}x^{2} - 2ax - 63$.
Printed answer:
- $(ax + 7)(ax - 9)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a*x + 7)*(a*x - 9)
Exercise 38, problem 31, p. 82
$a^{2} + 2ax - 63x^{2}$.
Printed answer:
- $(a - 7x)(a + 9x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 7*x)*(a + 9*x)
Exercise 38, problem 32, p. 82
$a^{2} - 9ab + 20b^{2}$.
Printed answer:
- $(a - 4b)(a - 5b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 4*b)*(a - 5*b)
Exercise 38, problem 33, p. 82
$x^{2}y^{2} - 19xyz + 48z^{2}$.
Printed answer:
- $(xy - 3z)(xy - 16z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x*y - 3*z)*(x*y - 16*z)
Exercise 38, problem 34, p. 82
$a^{2}b^{2} + 15abc + 44c^{2}$.
Printed answer:
- $(ab + 4c)(ab + 11c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a*b + 4*c)*(a*b + 11*c)
Exercise 38, problem 35, p. 82
$x^{2} - 13xy + 36y^{2}$.
Printed answer:
- $(x - 4y)(x - 9y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 4*y)*(x - 9*y)
Exercise 38, problem 36, p. 82
$x^{2} + 19xy + 84y^{2}$.
Printed answer:
- $(x + 7y)(x + 12y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 7*y)*(x + 12*y)
Exercise 38, problem 37, p. 82
$a^{2}x^{2} - 23axy + 102y^{2}$.
Printed answer:
- $(ax - 6y)(ax - 17y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a*x - 6*y)*(a*x - 17*y)
Exercise 38, problem 38, p. 82
$x^{4} - 9x^{2}y^{2} + 20y^{4}$.
Printed answer:
- $(x + 2y)(x - 2y)(x^{2} - 5y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 2*y)*(x - 2*y)*(x**2 - 5*y**2)
Exercise 38, problem 39, p. 82
$a^{4}x^{4} - 24a^{2}x^{2}y^{2} + 143y^{4}$.
Printed answer:
- $(a^{2}x^{2} - 11y^{2})(a^{2}x^{2} - 13y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a**2*x**2 - 11*y**2)*(a**2*x**2 - 13*y**2)
Exercise 38, problem 4, p. 82
$a^{2} - 6a + 5$.
Printed answer:
- $(a - 1)(a - 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 1)*(a - 5)
Exercise 38, problem 40, p. 82
$a^{6}b^{6} - 23a^{3}b^{3}c^{2} + 132c^{4}$.
Printed answer:
- $(a^{3}b^{3} - 11c^{2})(a^{3}b^{3} - 12c^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a**3*b**3 - 11*c**2)*(a**3*b**3 - 12*c**2)
Exercise 38, problem 41, p. 82
$a^{2} - 20abc - 96b^{2}c^{2}$.
Printed answer:
- $(a + 4bc)(a - 24bc)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 4*b*c)*(a - 24*b*c)
Exercise 38, problem 42, p. 82
$a^{2} - 4abc - 96b^{2}c^{2}$.
Printed answer:
- $(a + 8bc)(a - 12bc)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 8*b*c)*(a - 12*b*c)
Exercise 38, problem 43, p. 82
$a^{2} - 10abc - 96b^{2}c^{2}$.
Printed answer:
- $(a + 6bc)(a - 16bc)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 6*b*c)*(a - 16*b*c)
Exercise 38, problem 44, p. 82
$a^{2} + 29abc - 96b^{2}c^{2}$.
Printed answer:
- $(a - 3bc)(a + 32bc)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 3*b*c)*(a + 32*b*c)
Exercise 38, problem 45, p. 82
$a^{2} - 46abc - 96b^{2}c^{2}$.
Printed answer:
- $(a + 2bc)(a - 48bc)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 2*b*c)*(a - 48*b*c)
Exercise 38, problem 46, p. 82
$a^{2} + 49abc + 48b^{2}c^{2}$.
Printed answer:
- $(a + bc)(a + 48bc)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + b*c)*(a + 48*b*c)
Exercise 38, problem 47, p. 82
$x^{2} - 18xyz - 243y^{2}z^{2}$.
Printed answer:
- $(x + 9yz)(x - 27yz)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 9*y*z)*(x - 27*y*z)
Exercise 38, problem 48, p. 82
$x^{2}y^{2} - xyz - 182z^{2}$.
Printed answer:
- $(xy + 13z)(xy - 14z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x*y + 13*z)*(x*y - 14*z)
Exercise 38, problem 5, p. 82
$a^{2} + 4a - 5$.
Printed answer:
- $(a - 1)(a + 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 1)*(a + 5)
Exercise 38, problem 6, p. 82
$a^{2} - 4a - 5$.
Printed answer:
- $(a + 1)(a - 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 1)*(a - 5)
Exercise 38, problem 7, p. 82
$c^{2} - 9c + 18$.
Printed answer:
- $(c - 3)(c - 6)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (c - 3)*(c - 6)
Exercise 38, problem 8, p. 82
$c^{2} + 9c + 18$.
Printed answer:
- $(c + 3)(c + 6)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (c + 3)*(c + 6)
Exercise 38, problem 9, p. 82
$c^{2} + 3c - 18$.
Printed answer:
- $(c - 3)(c + 6)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (c - 3)*(c + 6)

Exercise 39

Exercise 39, problem 1, p. 83
$a^{3} - 7a$.
Printed answer:
- $a(a^{2} - 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes a*(a**2 - 7)
Exercise 39, problem 10, p. 83
$x^{2} - 2x - 3$.
Printed answer:
- $(x + 1)(x - 3)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 1)*(x - 3)
Exercise 39, problem 11, p. 83
$x^{2} + 4x - 21$.
Printed answer:
- $(x - 3)(x + 7)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3)*(x + 7)
Exercise 39, problem 12, p. 83
$a^{2} - 11a - 26$.
Printed answer:
- $(a + 2)(a - 13)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 2)*(a - 13)
Exercise 39, problem 13, p. 83
$ax^{2} + bx^{2} + 3a + 3b$.
Printed answer:
- $(x^{2} + 3)(a + b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x**2 + 3)*(a + b)
Exercise 39, problem 14, p. 83
$x^{2} - 3x- xy + 3y$.
Printed answer:
- $(x - 3)(x - y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3)*(x - y)
Exercise 39, problem 15, p. 83
$x^{2} - 7x + 12$.
Printed answer:
- $(x - 3)(x - 4)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3)*(x - 4)
Exercise 39, problem 16, p. 83
$a^{2} + 5ab + 6b^{2}$.
Printed answer:
- $(a + 2b)(a + 3b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 2*b)*(a + 3*b)
Exercise 39, problem 17, p. 83
$x^{4} + 10x^{2} + 25$.
Printed answer:
- $(x^{2} + 5)(x^{2} + 5)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x**2 + 5)*(x**2 + 5)
Exercise 39, problem 18, p. 83
$x^{2} - 18x + 81$.
Printed answer:
- $(x - 9)(x - 9)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 9)*(x - 9)
Exercise 39, problem 19, p. 83
$x^{2} - 21x + 110$.
Printed answer:
- $(x - 10)(x - 11)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 10)*(x - 11)
Exercise 39, problem 2, p. 83
$3a^{2}b^{2} - 2a^{3}b + 3ab^{3}$.
Printed answer:
- $ab(3ab - 2a^{2} + 3b^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes a*b*(3*a*b - 2*a**2 + 3*b**2)
Exercise 39, problem 20, p. 83
$x^{2} + 19x + 88$.
Printed answer:
- $(x + 8)(x + 11)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 8)*(x + 11)
Exercise 39, problem 21, p. 83
$x^{2} - 19x + 88$.
Printed answer:
- $(x - 8)(x + 11)$.
unverified: no computed check settled this one (yet)
How it was checked
- factor: the printed answer does not match the problem (x - 8)*(x + 11)
Exercise 39, problem 22, p. 83
$x^{3} - x^{2} + x - 1$.
Printed answer:
- $(x^{2} + 1)(x - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x**2 + 1)*(x - 1)
Exercise 39, problem 23, p. 83
$9x^{4} - x^{2}$.
Printed answer:
- $x^{2}(3x + 1)(3x - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes x**2*(3*x + 1)*(3*x - 1)
Exercise 39, problem 24, p. 83
$1 - (a - b)^{2}$.
Printed answer:
- $(1 + a - b)(1 - a + b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (1 + a - b)*(1 - a + b)
Exercise 39, problem 25, p. 83
$(a^{3} + b^{3}) + (a + b)$.
Printed answer:
- $(a + b)(a^{2} - ab + b^{2} + 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + b)*(a**2 - a*b + b**2 + 1)
Exercise 39, problem 26, p. 83
$m^{2}x - n^{2}x + m^{2}y - n^{2}y$.
Printed answer:
- $(m + n)(m - n)(x + y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (m + n)*(m - n)*(x + y)
Exercise 39, problem 27, p. 83
$(x - y)^{2} - z^{2}$.
Printed answer:
- $(x - y + z)(x - y - z)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - y + z)*(x - y - z)
Exercise 39, problem 28, p. 83
$z^{2} - (x - y)^{2}$.
Printed answer:
- $(z + x - y)(z - x + y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (z + x - y)*(z - x + y)
Exercise 39, problem 29, p. 83
$4a^{4} - (3a - 1)^{2}$.
Printed answer:
- $(2a^{2} + 3a - 1)(2a^{2} - 3a + 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*a**2 + 3*a - 1)*(2*a**2 - 3*a + 1)
Exercise 39, problem 3, p. 83
$(a - b)^{2} + (a - b)$.
Printed answer:
- $(a - b + 1)(a - b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - b + 1)*(a - b)
Exercise 39, problem 30, p. 83
$8x^{3} - y^{3}$.
Printed answer:
- $(2x - y)(4x^{2} + 2xy + y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (2*x - y)*(4*x**2 + 2*x*y + y**2)
Exercise 39, problem 31, p. 83
$x^{3} - 3x^{2}y$.
Printed answer:
- $x^{2}(x - 3y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes x**2*(x - 3*y)
Exercise 39, problem 32, p. 83
$x^{3} - 27y^{3}$.
Printed answer:
- $(x - 3y)(x^{2} + 3xy + 9y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 3*y)*(x**2 + 3*x*y + 9*y**2)
Exercise 39, problem 33, p. 83
$x^{2} + 3x - 40$.
Printed answer:
- $(x - 5)(x + 8)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 5)*(x + 8)
Exercise 39, problem 34, p. 83
$x^{2} + 3xy - 10y^{2}$.
Printed answer:
- $(x - 2y)(x + 5y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 2*y)*(x + 5*y)
Exercise 39, problem 35, p. 83
$1 - 16x^{2}$.
Printed answer:
- $(1 + 4x)(1 - 4x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (1 + 4*x)*(1 - 4*x)
Exercise 39, problem 36, p. 83
$a^{6} - 9a^{2}b^{4}$.
Printed answer:
- $a^{2}(a^{2} + 3b^{2})(a^{2} - 3b^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes a**2*(a**2 + 3*b**2)*(a**2 - 3*b**2)
Exercise 39, problem 37, p. 83
$x^{3} + 3x^{2}y + 2xy^{2}$.
Printed answer:
- $x(x + y)(x + 2y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes x*(x + y)*(x + 2*y)
Exercise 39, problem 38, p. 83
$x^{4} + 4x^{3}y + 3x^{2}y^{2}$.
Printed answer:
- $x^{2}(x + y)(x + 3y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes x**2*(x + y)*(x + 3*y)
Exercise 39, problem 39, p. 83
$x^{2} - 4xy^{2} + 4y^{4}$.
Printed answer:
- $(x - 2y^{2})(x - 2y^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x - 2*y**2)*(x - 2*y**2)
Exercise 39, problem 4, p. 83
$(a + b)^{2} - 1$.
Printed answer:
- $(a + b + 1)(a + b - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + b + 1)*(a + b - 1)
Exercise 39, problem 40, p. 83
$16x^{4} + 8x^{2} + 1$.
Printed answer:
- $(4x^{2} + 1)(4x^{2} + 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (4*x**2 + 1)*(4*x**2 + 1)
Exercise 39, problem 41, p. 83
$9a^{4} - 4a^{2}c^{2}$.
Printed answer:
- $a^{2}(3a + 2c)(3a - 2c)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes a**2*(3*a + 2*c)*(3*a - 2*c)
Exercise 39, problem 42, p. 83
$a^{3}b - a^{2}b^{2} - 2ab^{3}$.
Printed answer:
- $ab(a + b)(a - 2b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes a*b*(a + b)*(a - 2*b)
Exercise 39, problem 43, p. 83
$x^{4} - x^{3} + 8x - 8$.
Printed answer:
- $(x + 2)(x^{2} - 2x + 4)(x - 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 2)*(x**2 - 2*x + 4)*(x - 1)
Exercise 39, problem 44, p. 83
$a^{4} - a^{3}x + ay^{3} - xy^{3}$.
Printed answer:
- $(a + y)(a^{2} - ay + y^{2})(a - x)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + y)*(a**2 - a*y + y**2)*(a - x)
Exercise 39, problem 5, p. 83
$a^{3} + 8b^{3}$.
Printed answer:
- $(a + 2b)(a^{2} - 2ab + 4b^{2})$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a + 2*b)*(a**2 - 2*a*b + 4*b**2)
Exercise 39, problem 6, p. 83
$(x^{2} - 4y^{2}) + (x - 2y)$.
Printed answer:
- $(x + 2y + 1)(x - 2y)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 2*y + 1)*(x - 2*y)
Exercise 39, problem 7, p. 83
$(a^{3} - b^{3}) + (a - b)$.
Printed answer:
- $(a - b)(a^{2} + ab + b^{2} + 1)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - b)*(a**2 + a*b + b**2 + 1)
Exercise 39, problem 8, p. 83
$a^{2} - 6ab + 9b^{2}$.
Printed answer:
- $(a - 3b)(a - 3b)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (a - 3*b)*(a - 3*b)
Exercise 39, problem 9, p. 83
$x^{2} - x -2$.
Printed answer:
- $(x + 1)(x - 2)$.
verified: the printed answer passed a computed check
How it was checked
- factor: passes (x + 1)*(x - 2)