# How do you use polynomial synthetic division to divide (x^3+8)div(x+2) and write the polynomial in the form p(x)=d(x)q(x)+r(x)?

##### 1 Answer
Jul 21, 2017

${x}^{2} - 2 x + 4$

#### Explanation:

Let's use the formula :

${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$

$\frac{{x}^{3} + 8}{x + 2} = \frac{{x}^{3} + {2}^{3}}{x + 2} = \frac{\cancel{\left(x + 2\right)} \left({x}^{2} - 2 x + 4\right)}{\cancel{x + 2}} =$

${x}^{2} - 2 x + 4$