Let f(x) = 5x3 − x2 − 60x + 12 and g(x) = 5x − 1. Find f of x over g of x. A. x2 − 12

B. 5x2 + 4x

C. x2 − 12x

D. 5x2 + 4

A

(5x^3 - x^2 - 60x + 12)/(5x-1)

First, I’m going to factor the top. I’m going to factor by grouping.

The GCF of 5x^3 - x^2 is x^2. I pull x^2 out and am left with x^2(5x-1)
The GCF of 60x-12 is 12. I pull out 12 and am left with -12(5x-1). The fully factored expression looks like this:
(x^2-12)(5x-1)

I am now left with (x^2-12)(5x-1)/5x-1.

The 5x-1s cancel out. I am left with x^2 - 12