# How do you factor x^2-8x-48?

Apr 5, 2016

${x}^{2} - 8 x - 48 = \left(x + 4\right) \left(x - 12\right)$

#### Explanation:

To factorize a polynomial of general form $a {x}^{2} + b x + c$, one should divide middle term $b x$ in two parts, whose sum is $b$ and product is $a \times c$.

So for ${x}^{2} - 8 x - 48$, we should divide $- 8 x$ in two parts which add up to $- 8$ and whose product is $1 \times \left(- 48\right) = - 48$.

A few trial indicate them to be $- 12$ and $4$. Hence

${x}^{2} - 8 x - 48 = {x}^{2} - 12 x + 4 x - 48$ or

$x \left(x - 12\right) + 4 \left(x - 12\right)$ or

$\left(x + 4\right) \left(x - 12\right)$