Question

question
factor.
$x^2 - 5x - 14$

Explanation:

Step1: Find pair of factors of -14

We need two numbers that multiply to $-14$ and add to $-5$. The numbers are $-7$ and $2$, since $(-7)\times2=-14$ and $-7+2=-5$.

Step2: Split middle term & factor by grouping

Rewrite the quadratic using the found pair, then group and factor:

$$\begin{align*} x^2 - 5x - 14&=x^2 -7x +2x -14\\ &=x(x-7)+2(x-7)\\ &=(x-7)(x+2) \end{align*}$$

Answer:

$(x-7)(x+2)$