# How do you factor 6x^3-48?

May 3, 2018

$6 \left(x - 2\right) \left({x}^{2} + 2 x + 4\right)$

#### Explanation:

To factor, we have to find the GCF, or Greatest Common Factor. This means the largest factor that both expressions have.

Therefore, the GCF is $6$. So when we factor it becomes:
$6 \left({x}^{3} - 8\right)$

We can still factor this further.

$\left({x}^{3} - 8\right)$ is in the form ${a}^{3} - {b}^{3}$, which factors down to $\left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

Therefore, that becomes:
$\left(x - 2\right) \left({x}^{2} + 2 x + 4\right)$

So the completely factored answer is:
$6 \left(x - 2\right) \left({x}^{2} + 2 x + 4\right)$

Hope this helps!