# How do you factor 5c^2 + 12c + 7?

Jun 30, 2015

Use the $a \cdot c$ method of factoring.

#### Explanation:

$5 {c}^{2} + 12 c + 7$ is in the form $a {x}^{2} + b x + c$, where a=5; b=12; and $c = 7$.

Multiply $a \cdot c$, and find two factors that when added equal $b$.

$a \cdot c = 5 \cdot 7 = 35$

Find two factors of $35$ that when added equal $12$.

$5$ and $7$ fit the criteria. $5 + 7 = 12$

Rewrite $12 c$ as $5 c$ and $7 c$.

Rewrite the expression.

$5 {c}^{2} + 5 c + 7 c + 7$

Divide the expression into two groups.

$\left(5 {c}^{2} + 5 c\right) + \left(7 c + 7\right)$

Factor out the $5 c$ from the first group, and the $7$ from the second group.

$5 c \left(c + 1\right) + 7 \left(c + 1\right)$

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

$\left(c + 1\right) \left(5 c + 7\right)$