Question

In the following exercises, factor completely.

$6u^2+3u-18$

Short answer

On factoring, we get $3\left(2u-3\right)\left(u+2\right)$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$6u^2+3u-18$

Factor out the GCF,

$=3\left(2u^2+u-6\right)$

Step 2. Simplify the expression.

On simplifying, we get,

$$\begin{gathered} =3\left(2u^2+4u-3u-6\right) \\ =3\{2u\left(u+2\right)-3\left(u+2\right)\} \\ =3\left(2u-3\right)\left(u+2\right) \end{gathered}$$

Step 3. Check the answers.

Check by multiplying,

$$\begin{gathered} =3\left(2u-3\right)\left(u+2\right) \\ =3\left(2u^2+4u-3u-6\right) \\ =3\left(2u^2+u-6\right) \\ =6u^2+3u-18 \end{gathered}$$

This is true.