Question

In the following exercises, factor each expression using any method$6r^2+30r+36$

Short answer

The factors are$6\left(r+3\right)\left(r+2\right)$.

Step-by-step solution

Step 1. Given Information

The trinomial is$6r^2+30r+36$

Find factors

Step 2. Find GCF 

Find GCF from $6r^2+30r+36$and factor it

GCF is 6

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

Step 3. Factor the trinomial inside the parenthesis

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

So the numbers are 2 and 3

Trinomial becomes $6\left(r^2+3r+2r+6\right)$

Factor it

localid="1645525480797" $6\left(r+3\right)\left(r+2\right)$

Step 4. Check

Multiply the factors $6\left(r+2\right)\left(r+3\right)$

$$\begin{gathered} 6\left(r^2+2r+3r+6\right) \\ 6\left(r^2+5r+6\right) \\ 6r^2+30r+36 \end{gathered}$$