Question

What is the quotient (x3 + 8) ÷ (x + 2)? x2 + 2x + 4 x2 – 2x + 4 x2 + 4 x2 – 4

Answer 1

Answer:

$x^2-2x+4$

Step-by-step explanation:

The given expression is

$\frac{x^3+8}{x+2}$

Recall and use the following property to factor the numerator;

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$\frac{x^3+2^3}{x+2}=\frac{(x+2)(x^2-2x+2^2)}{(x+2)}$

This will give us;

$\frac{x^3+2^3}{x+2}=\frac{(x+2)(x^2-2x+4)}{(x+2)}$

Simplify;

$\frac{x^3+2^3}{x+2}=x^2-2x+4$