Question

In the following exercises, factors completely:

$6u^2+3u-18$.

Short answer

The factors for the expression is,$3(u+2)(2u-3)$.

Step-by-step solution

Step 1. Given Information.

The expression is,

$6u^2+3u-18$.

Step 2. Factor completely.

Taking $3$common out,

$6u^2+3u-18=3(2u^2+u-6)$

Splitting the middle term such that the sum is $1$and the product is $(-12)$,

$3(2u^2+u-6)=3(2u^2+4u-3u-6)$

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