How do you divide (x^4 - 16) /( x + 2)?

Oct 26, 2015

The answer is$\left(x + 2\right) \left({x}^{2} + 4\right)$ = ${x}^{3} - 2 {x}^{2} + 4 x - 8$

Explanation:

Factorise $\left({x}^{4} - 16\right)$ as it is the difference of 2 squares
You then get
$\frac{\left({x}^{2} - 4\right) \left({x}^{2} + 4\right)}{x + 2}$

${x}^{2} - 4$ is also the difference of 2 squares and will factorise to $\left(x - 2\right) \left(x + 2\right)$
so this gives you $\frac{\left(x - 2\right) \left(x + 2\right) \left({x}^{2} + 4\right)}{x + 2}$
The $\left(x + 2\right)$ terms cancel out to give you
$\left(x - 2\right) \left({x}^{2} + 4\right)$