Question

Factor completely:

$p^2+pq-12q^2$.

Short answer

The factored polynomial is,

$(p+4q)(p-3q)$.

Step-by-step solution

Step 1. Given the information.

The polynomial function is,

$p^2+pq-12q^2$.

Step 2. Factoring the polynomial.

$p^2+pq-12q^2$

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

$=p^2+4pq-3pq-12q^2$

$=(p^2+4pq)-(3pq+12q^2)$

Finding the common factors,

$$\begin{gathered} =p(p+4q)-3q(p+4q) \\ =(p+4q)(p-3q) \end{gathered}$$

Step 3. Checking the solution.

$(p+4q)(p-3q)$

Multiplying the brackets,

$$\begin{gathered} =p(p-3q)+4q(p-3q) \\ =p^2-3pq+4pq-12q^2 \\ =p^2+pq-12q^2 \end{gathered}$$

This is true.