select all of the roots of x^3 + 2x^2 - 16x - 32. -1 -2 -4 1 4 5

Explanation:

Step1: Group the terms

$(x^{3}+2x^{2})-(16x + 32)$

Step2: Factor out common factors from each group

$x^{2}(x + 2)-16(x + 2)$

Step3: Factor out the common binomial factor

$(x + 2)(x^{2}-16)$

Step4: Factor the difference - of - squares

$(x + 2)(x + 4)(x - 4)$

Step5: Set each factor equal to zero and solve for x

$x+2=0\Rightarrow x=-2$; $x + 4=0\Rightarrow x=-4$; $x - 4=0\Rightarrow x = 4$

Answer:

-2, -4, 4