To solve this problem we will factor the given polynomial.
First, we rewrite the given equation as follows:
[tex]x^3+x^2-4x-4=0.[/tex]
Now, notice that:
[tex]x^3+x^2-4x-4=(x+1)(x+2)(x-2).[/tex]
Therefore:
[tex]\begin{gathered} x^3+x^2-4x-4=0\text{ if and only if} \\ \left(x+1\right)\left(x+2\right)\left(x-2\right)=0. \end{gathered}[/tex]
Recall that:
[tex]ab=0,\text{ if and only if a=0 or b=0.}[/tex]
Therefore:
[tex]\left(x+1\right)\left(x+2\right)\left(x-2\right)=0\text{ if \lparen x+1\rparen=0 or \lparen x+2\rparen=0 or \lparen x-2\rparen=0.}[/tex]
Solving each equation for x, we get:
[tex]x=-1,\text{ x=-2, x=2.}[/tex]
Answer:
[tex]?=-2.[/tex]
