Question

Factor by Grouping In the following exercises, factor by grouping.

$uv-9u+2v-18$

Short answer

The simplest polynomial is$(v-9)(u+2)$

Step-by-step solution

Step 1. Given

A polynomial is given as$uv-9u+2v-18$

Step 2. Concept Used

First we have to find the GCF (group common factor). Then we will factor out it after that we will group the given polynomial.

Step 3. Calculation

A polynomial is given as $uv-9u+2v-18$

First group the polynomial,

$uv-9u+2v-18=(uv-9u)+(2v-18)$

Factor out the GCF,

$$\begin{gathered} =u(v-9)+2(v-9) \\ =(v-9)(u+2) \end{gathered}$$

Step 4. Verification

Multiply the factors,

$$\begin{gathered} (v-9)(u+2)=vu+2v-9u-18 \\ =uv-9u+2v-18 \end{gathered}$$