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