Q. 256 - Intermediate Algebra

Question

In the following exercises, factor completely. 

$5q^2-15q-90$

Step-by-Step Solution

Answer

The required factors are $5(q-6)(q+3)$

Step 1. Given Information

The given expression is $5q^2-15q-90$

Step 2. Calculation

We will find the factors by taking common factor out and then use the middle term splitting method.

$$\begin{gathered} 5q^2-15q-90=5(q^2-3q-18) \\ =5(q^2-6q+3q-18) \\ =5\left(q\right(q-6)+3(q-6\left)\right) \\ =5(q-6)(q+3) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} 5(q-6)(q+3)=5\left(q\right(q-6)+3(q-6\left)\right) \\ =5(q^2-6q+3q-18) \\ =5(q^2-3q-18) \\ =5q^2-15q-90 \end{gathered}$$