Question

Given f(x)=4x^3+7x^2-7x-10 factor f(x), given that -1 is a zero

Answer 1

If - 1 is a zero then

`(x + 1)`
is a factor.

Dividing with this factor using the long division approach, we get the quadratic factor to be,


`4 {x}^(2) + 3x - 10`
(see attachment).

We can rewrite the polynomial as

`f(x) = (x + 1)(4 {x}^(2) + 3x - 10)`

We can further factor as


`f(x) = (x + 1)(4 {x}^(2) - 5x + 8x - 10)`
That is


`f(x) = (x + 1)(x + 2)(4x - 5)`