# How do you factor the trinomial  x^2-x-42?

Jul 5, 2018

$\left(x - 7\right) \left(x + 6\right)$

#### Explanation:

$\text{the factors of "-42" which sum to } - 1$
$\text{are "-7" and } + 6$

${x}^{2} - x - 42 = \left(x - 7\right) \left(x + 6\right)$

Jul 5, 2018

$\left(x - 7\right) \left(x + 6\right)$

#### Explanation:

Given: ${x}^{2} - x - 42$.

With some $\textcolor{b l u e}{\boldsymbol{m a g i c}}$, notice how it equals:

$= {x}^{2} - 7 x + 6 x - 42$

$= x \left(x - 7\right) + 6 \left(x - 7\right)$

$= \left(x - 7\right) \left(x + 6\right)$

The $\textcolor{b l u e}{\boldsymbol{m a g i c}}$ is that you pick two numbers, say $a$ and $b$, whose sum equals the coefficient of the middle term and whose product equals the last terms.

In other words, we get:

$a b = - 42$

$a + b = - 1$

Clearly, $- 7$ and $6$ are the numbers.