Question

Which of the following is a factor of 512x3 − 125?

8x + 5

64x2 + 80x + 25

64x2 + 40x + 25

None of the above

Answer 1

64x2 + 40x + 25

Explanation:

I got it right

Answer 2

`(64x^2+80x+25)`

Explanation:

The polynomial
`512x^3-125` has the form of a difference of cubes
`(a^3-b^3)`. This form factors into
`(a-b)(a^2+2ab+b^2)`.

512 is the cube of 8 so a=8. 125 is the cube 5 so b=5.

It factors as
`(a-b)(a^2+2ab+b^2)= (8x-5)(64x^2+80x+25)`.