# How do you factor completely: 5x^2 − 2x − 7?

##### 1 Answer
Jul 20, 2015

$5 {x}^{2} - 2 x - 7 = \left(5 x - 7\right) \left(x + 1\right)$

#### Explanation:

$5 {x}^{2} - 2 x - 7$ is a quadratic equation in the form $a {x}^{2} + b x + c$, in which $a = 5 , b = - 2 , \mathmr{and} c = - 7$.

This equation can be factored by the $a \cdot c$ method, also called splitting the middle, or factoring by grouping.

Multiply $a$ times $c$.

$5 \cdot - 7 = - 35$

Find two numbers that when multiplied equal $- 35$, and when added equal the coefficient of the center term, $b = - 2$.

The numbers $5$ and $- 7$ meet the criteria.

Rewrite the equation, replacing $- 2 x$ with the sum of $5 x$ and $- 7 x$.

$5 {x}^{2} + 5 x - 7 x - 7$

Group into two binomials.

$\left(5 {x}^{2} + 5 x\right) - \left(7 x - 7\right)$ =

Factor out the GCF from each group.

$5 x \left(x + 1\right) - 7 \left(x + 1\right)$

Factor out the common term $\left(x + 1\right)$.

$\left(5 x - 7\right) \left(x + 1\right)$