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

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