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

Answer:

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

Step-by-step 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  $(a-b)(a^2+2ab+b^2)= (8x-5)(64x^2+80x+25)$.