Question

Solve the polynomial equation by factoring and then using the zero product principle

Answer 1

Given;

$x^3+2x^2=16x+32$

To find: The equation in factored form and solution set.

Explanation:

Given equation can be written as

$x^3+2x^2-16x-32=0$$\begin{gathered} \text{When x=-2, The equation becomes,} \\ -8+8+32-32=0 \\ 0=0 \\ \text{Then (x+2) is a factor of given equation.} \end{gathered}$

By using the factor (x+2), We proceed with the synthetic division

$\begin{gathered} x^3+2x^2-16x-32=0 \\ (x+2)(x^2-16)=0 \\ (x+2)(x^2-4^2)=0 \\ (x+2)(x+4)(x-4)=0 \end{gathered}$

Therefore, the equation is factored form:

$(x+2)(x+4)(x-4)=0$

Then the solution set is

$\mleft\lbrace-2,-4,4\mright\rbrace$