# How do you factor completely 5x(x + 3) + 6(x + 3)?

May 17, 2016

#### Answer:

$\left(x + 3\right) \left(5 x + 6\right)$

#### Explanation:

They have already done a lot of the work for you.

The common factor is $\left(x + 3\right)$ so we factor that out giving:

$\textcolor{b l u e}{\left(x + 3\right)} \textcolor{b r o w n}{\left(5 x \textcolor{g r e e n}{+} 6\right)}$

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To emphasise how this works:

Consider the example $\textcolor{b l u e}{a} \textcolor{b r o w n}{\left(b \textcolor{g r e e n}{+} c\right)}$

This is saying multiply everything inside the brackets by $a$.

So you have $\textcolor{b r o w n}{\textcolor{b l u e}{a \times} b \textcolor{g r e e n}{+} \textcolor{b l u e}{a \times} c}$

Notice that the $\textcolor{g r e e n}{+}$ is still kept between.

now think of $a \text{ as "(x+3)}$

$\textcolor{b r o w n}{\textcolor{b l u e}{\left(x + 3\right) \times} 5 x \textcolor{g r e e n}{+} \textcolor{b l u e}{\left(x + 3\right) \times} 6}$