Answer:
[tex]x^2-2x+4[/tex]
Step-by-step explanation:
The given expression is
[tex]\frac{x^3+8}{x+2}[/tex]
Recall and use the following property to factor the numerator;
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]\frac{x^3+2^3}{x+2}=\frac{(x+2)(x^2-2x+2^2)}{(x+2)}[/tex]
This will give us;
[tex]\frac{x^3+2^3}{x+2}=\frac{(x+2)(x^2-2x+4)}{(x+2)}[/tex]
Simplify;
[tex]\frac{x^3+2^3}{x+2}=x^2-2x+4[/tex]
