# How do you factor 5x^2+27x+36?

Aug 14, 2016

$\left(5 x + 12\right) \left(x + 3\right)$

#### Explanation:

Read all the clues and information from the signs and numbers.

$\textcolor{g r e e n}{5} {x}^{2} \textcolor{b l u e}{+} \textcolor{m a \ge n t a}{27} x \textcolor{red}{+} \textcolor{g r e e n}{36}$

Find factors of $\textcolor{g r e e n}{5 \mathmr{and} 36}$ which $\textcolor{red}{A D D}$ to give $\textcolor{m a \ge n t a}{27} .$

The signs are $\textcolor{red}{\text{the SAME}}$ , they are $\textcolor{b l u e}{\text{both positive}}$

Choose factors and find the cross-products.
A bit of trial and error will result in the following.

$\textcolor{w h i t e}{\ldots \ldots .} 5 \text{ } 12 \Rightarrow 1 \times 12 = 12$
$\textcolor{w h i t e}{\ldots \ldots .} 1 \text{ "3 rArr 5 xx3 + 15" } 12 + 15 = 27$

The top row is the first bracket, the second row is the second row.

$\left(5 x + 12\right) \left(x + 3\right)$