Question

How do you factor `x^3-x^2-10x-8`?

Answer 1

`f(x) = (x + 1)(x + 2)(x - 4)`

Explanation:

f(x) = x^3 - x^2 - 10x - 8.
We find out that
f(-1) = -1 -1 + 10 - 8 = 0,
then, one factor is (x + 1).
After division -->
`f(x) = (x + 1)(x^2 - 2x - 8)`
The trinomial in parentheses can be factored.
Find 2 numbers knowing sum (-2) and product (-8).
They are (2) and (-4)
`(x^2 - 2x - 8) = (x + 2)(x - 4)`
`f(x) = (x + 1)(x + 2)( x - 4)`