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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 147E (page 1069)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information

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

Find factors

02

Step 2. Find GCF

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

GCF is 6

So, $6 (r^{2} + 5 r + 6)$

03

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 $6 (r^{2} + 3 r + 2 r + 6)$

Factor it

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

04

Step 4. Check

Multiply the factors $6 (r + 2) (r + 3)$

$6 (r^{2} + 2 r + 3 r + 6) 6 (r^{2} + 5 r + 6) 6 r^{2} + 30 r + 36$

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