GREATEST COMMON FACTOR

Exercise 39

1. Exercise 39, problem 1

   $3a^4 b^3 + 6a^2 b^5$ and $9a^3 b^2 + 18 a b^3$.

   Printed answer:

   • $3ab^2$.

   verified: the printed answer passed a computed check

   How it was checked

   • hcf: passes 3*a*b**2

2. Exercise 39, problem 10

   $y^3 - y$, $y^3 + 9y^2 - 10y$, and $y^4-y$.

   Printed answer:

   • $y\left(y-1\right)$.

   verified: the printed answer passed a computed check

   How it was checked

   • hcf: passes y*(y - 1)

3. Exercise 39, problem 11

   $x^2 - y^2$, $xy - y^2 + xz - yz$, and $x^3 - x^2 y + xy^2 - y^3$.

   Printed answer:

   • $x-y$.

   verified: the printed answer passed a computed check

   How it was checked

   • hcf: passes x - y

4. Exercise 39, problem 12

   $3a c^5 d^3 - 3a c^2 - 3a^3 c^3 d^3 + 3a3$ and $9a^2 c^4 - 9a^6$.

   Printed answer:

   • $3a\left(c^2-a^2\right)$.

   verified: the printed answer passed a computed check

   How it was checked

   • hcf: passes 3*a*(c**2 - a**2)

5. Exercise 39, problem 13

   $64x^{11} - 8x^2 y^6$ and $12x^8 + 3x^2 y^4 - 12x^5 y^2$.

   Printed answer:

   • $x^2\left(2x^3-y^2\right)$.

   verified: the printed answer passed a computed check

   How it was checked

   • hcf: passes x**2*(2*x**3 - y**2)

6. Exercise 39, problem 14

   A merchant mixes $a$ pounds of tea worth $x$ cents a pound with $b$ pounds worth $y$ cents a pound. How much is the mixture worth per pound?

   Printed answer:

   • $\displaystyle \frac{ax+by}{a+b}$ cts.

   unverified: no computed check settled this one (yet)

   How it was checked

   • other: not a kind the checker handles (a*x + b*y)/(a + b)

7. Exercise 39, problem 15

   If a man bought a horse for $x$ dollars and sold him so as to gain $5 \%$, what will represent the number of dollars he gained?

   Printed answer:

   • $\displaystyle \frac{5}{100}x$ dols.

   unverified: no computed check settled this one (yet)

   How it was checked

   • other: not a kind the checker handles Rational(5,100)*x

8. Exercise 39, problem 16

   The difference between two numbers is 6, and if 4 be added to the greater, the result will be three times the smaller. What are the numbers?

   Printed answer:

   • 5; 11.

   verified: the printed answer passed a computed check

   How it was checked

   • solve: passes {x: 11, y: 5}

9. Exercise 39, problem 2

   $5 x^5 y - 15 x^2 y^2$ and $15x^3 y^3 - 45 x y^5$.

   Printed answer:

   • $5xy$.

   verified: the printed answer passed a computed check

   How it was checked

   • hcf: passes 5*x*y

10. Exercise 39, problem 3

    $2x^5 y^4 + 2x^2 y^7$ and $6 x^3 y^3 - 6x y^5$.

    Printed answer:

    • $2xy^3\left(x+y\right)$.

    verified: the printed answer passed a computed check

    How it was checked

    • hcf: passes 2*x*y**3*(x + y)

11. Exercise 39, problem 4

    $3a^6 b - 3a^3 b^4$ and $12a^4 b^4 - 12a^2 b^6$.

    Printed answer:

    • $3a^2b\left(a-b\right)$.

    verified: the printed answer passed a computed check

    How it was checked

    • hcf: passes 3*a**2*b*(a - b)

12. Exercise 39, problem 5

    $mx - ma - nx + na$ and $m^3 - n^3$.

    Printed answer:

    • $m-n$.

    verified: the printed answer passed a computed check

    How it was checked

    • hcf: passes m - n

13. Exercise 39, problem 6

    $81 x^8 - 16$ and $81x^8-72x^4 + 16$.

    Printed answer:

    • $9x^4-4$.

    verified: the printed answer passed a computed check

    How it was checked

    • hcf: passes 9*x**4 - 4

14. Exercise 39, problem 7

    $x^2 - 20 - x$, $3x^2 - 24 x + 45$, and $x^2 - 5x$.

    Printed answer:

    • $x-5$.

    verified: the printed answer passed a computed check

    How it was checked

    • hcf: passes x - 5

15. Exercise 39, problem 8

    $x^2 +x -6$, $x^2-15 - 2x$, and $3x^2-27$.

    Printed answer:

    • $x+3$.

    verified: the printed answer passed a computed check

    How it was checked

    • hcf: passes x + 3

16. Exercise 39, problem 9

    $a^4 - 16$, $a2 -a -6$, and $(a^2 -4)^2$.

    Printed answer:

    • $a+2$.

    verified: the printed answer passed a computed check

    How it was checked

    • hcf: passes a + 2