Given;
[tex]x^3+2x^2=16x+32[/tex]
To find: The equation in factored form and solution set.
Explanation:
Given equation can be written as
[tex]x^3+2x^2-16x-32=0[/tex][tex]\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}[/tex]
By using the factor (x+2), We proceed with the synthetic division
[tex]\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}[/tex]
Therefore, the equation is factored form:
[tex](x+2)(x+4)(x-4)=0[/tex]
Then the solution set is
[tex]\mleft\lbrace-2,-4,4\mright\rbrace[/tex]
