# How do you factor the expression x^2 - x -6?

Mar 4, 2018

The factored expression $\left(x + 2\right) \left(x - 3\right)$.

#### Explanation:

First, find two numbers that multiply to $- 6$ (the $c$ value of the quadratic) and add up $- 1$ (the $b$ value of the quadratic).

The two numbers are $- 3$ and $2$. Now, split $- x$ into $- 3 x$ and $2 x$. Then, group together the two factors:

$\textcolor{w h i t e}{=} {x}^{2} - x - 6$

$= {x}^{2} - 3 x + 2 x - 6$

$= \textcolor{red}{x} \cdot x - \textcolor{red}{x} \cdot 3 + 2 x - 6$

$= \textcolor{red}{x} \cdot x - \textcolor{red}{x} \cdot 3 + \textcolor{b l u e}{2} \cdot x - \textcolor{b l u e}{2} \cdot 3$

$= \textcolor{red}{x} \left(x - 3\right) + \textcolor{b l u e}{2} \cdot x - \textcolor{b l u e}{2} \cdot 3$

$= \textcolor{red}{x} \left(x - 3\right) + \textcolor{b l u e}{2} \left(x - 3\right)$

$= \left(\textcolor{red}{x} + \textcolor{b l u e}{2}\right) \left(x - 3\right)$