Q. 144E - Intermediate Algebra

Question

In the following exercises, factor each expression using any method $5r^2+25r+30$

Step-by-Step Solution

Answer

The factors are $5\left(r+2\right)\left(r+3\right)$

Step 1. Given Information

The trinomial is $5r^2+25r+30$

Find factors.

Step 2. Find GCF

The GCF of trinomial $5r^2+25r+30$ is 5

So trinomial becomes

$5\left(r^2+5r+6\right)$

Step 3. Split the middle term of trinomial inside the parenthesis

Find two numbers such as product is 6 and sum is 5.

So the number are 2,3

So trinomial becomes

$$\begin{gathered} 5\left(r^2+2r+3r+6\right) \\ 5\left(r+2\right)\left(r+3\right) \end{gathered}$$

Step 4. Check

Multiply the factors $5\left(r+2\right)\left(r+3\right)$

$$\begin{gathered} 5\left(r^2+3r+2r+6\right) \\ 5\left(r^2+5r+6\right) \\ 5r^2+25r+30 \end{gathered}$$