Question

How do you factor `h(x)= x^3 + 2x^2 - 5x - 6`?

Answer 1

Find `h(-1) = 0`, then divide `h(x)` by `(x+1)` to find the other factors.

Explanation:

First note that `h(-1) = -1+2+5-6=0`, so `(x+1)` is a factor of `h(x)`

Divide `h(x)` by `(x+1)` using synthetic division:

So:

`x^3+2x^2-5x-6 = (x+1)(x^2+x-6) = (x+1)(x+3)(x-2)`