Question

In the following exercises, factor completely.

$15pq-15p+12q-12$

Short answer

The factored form of the polynomial is$3\left(5p+4\right)\left(q-1\right).$

Step-by-step solution

Step 1. Given Information.

The given polynomial is $15pq-15p+12q-12.$

Step 2. Factoring

Let's find the GCF and factor out the GCF,

$3\left(5pq-5p+4q-4\right)$

In the parentheses, the polynomial has more than three terms.

To factor, the given polynomial we will use the grouping method.

So,

$$\begin{gathered} 3\left(5pq-5p+4q-4\right) \\ =3\left[5p\left(q-1\right)+4\left(q-1\right)\right] \\ =3\left(5p+4\right)\left(q-1\right) \end{gathered}$$

The polynomial is factored completely.

Thus, the factored form is $3\left(5p+4\right)\left(q-1\right).$

Step 3. Check the answer

To check the answer, expand the factored form we get,

$$\begin{gathered} 15pq-15p+12q-12=3\left(5p+4\right)\left(q-1\right) \\ 15pq-15p+12q-12=3\left(5pq-5p+4q-4\right) \\ 15pq-15p+12q-12=15pq-15p+12q-12 \end{gathered}$$

L.H.S = R.H.S

Thus, the answer is right.