Question

In the following exercises, factor each expression using any method$q^2-29qr-96r^2$

Short answer

The factor are$\left(q+3r\right)\left(q-32r\right)$

Step-by-step solution

Step 1. Given Information

The trinomial is $q^2-29qr-96r^2$

Find factors by splitting middle term

Step 2. Factor the trinomial

Split the middle term of trinomial to find factors

Find two numbers such as their product is $-96$and sum is $-29$

The number are $-32$and $3$

$$\begin{gathered} q^2+3qr-32qr-96r^2 \\ q\left(q+3r\right)-32r\left(q+3r\right) \\ \left(q+3r\right)\left(q-32r\right) \end{gathered}$$

Step 3. Check

Multiply the factor $\left(q+3r\right)\left(q-32r\right)$

$$\begin{gathered} q^2+3qr-32qr-96r^2 \\ {q}^2-29qr-96r^2 \end{gathered}$$