Question

select all zeros of the polynomial function.
( h(x) = x^3 + 5x^2 - 4x - 20 )

Explanation:

Step1: Factor by grouping

$h(x) = x^3 + 5x^2 - 4x - 20 = x^2(x+5) - 4(x+5) = (x^2 - 4)(x+5)$

Step2: Factor difference of squares

$x^2 - 4 = (x-2)(x+2)$, so $h(x) = (x-2)(x+2)(x+5)$

Step3: Set h(x)=0, solve for x

$x-2=0 \implies x=2$; $x+2=0 \implies x=-2$; $x+5=0 \implies x=-5$

Answer:

-5, -2, 2