Q. 6.84 - Intermediate Algebra

Question

Factor completely: $6p{q}^2-9pq-6p$

Step-by-Step Solution

Answer

The required factors are $3(q-2)(2pq+p)$

Step 1. Given Information

The given expression is $6p{q}^2-9pq-6p$

Step 2. Calculation

We will factor the expression by taking the common factor outside the paranthesis and then use the middle term splitting method.

$$\begin{gathered} 6p{q}^2-9pq-6p=3[2p{q}^2-3pq-2p] \\ =3[2p{q}^2-4pq+pq-2p] \\ =3\left[2pq\right(q-2)+p(q-2\left)\right] \\ =3(q-2)(2pq+p) \end{gathered}$$

Step 3. Check

We will verify by multiplying the factors.

$$\begin{gathered} 3(q-2)(2pq+p)=3\left[2pq\right(q-2)+p(q-2\left)\right] \\ =3[2p{q}^2-4pq+pq-2p] \\ =3[2p{q}^2-3pq-2p] \\ =6p{q}^2-9pq-6p \end{gathered}$$