I need answers to my homework plz!

Question

1.) Carlos factored the polynomial, as shown below. Explain the error and enter the correct solution.

(8x^3-125)=(2x-5)^3

2.) List all of the possible rational zeros of f(x)=8x^3-2x^2+4x+4 by using the rational zero theorem.

Answer 1

1) This expression is the difference of cubes (a-b)^3 with a=2x and b=5 \

this factors to (2x-5)( 4x^2+10x +25)

2) The rational zero theorem states that all the possible rational zeros can be found by dividing all the factors of the final term by the factors of the leading term

factors of 4 are +/- 1,2,4

factors of 8 are +/- 1,2,4,8

this gives us +/-(1) +/-(1/2), +/-(1/4), +/-(1/8) +/-(2), +/-(4)