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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q 125. (page 590)

In the following exercises, factor using the 鈥榓c鈥� method. $48 y^{2} + 12 y 鈭� 36$

Short Answer

Expert verified

The factors are $12 (y + 1) (4 y - 3)$

Step by step solution

01

Step 1. Given information

The trinomial is $48 y^{2} + 12 y - 36$

Find factors of trinomial.

02

Step 2. Find the GCF

The common factor is 12.

Take factor from $48 y^{2} + 12 y - 36$

Trinomial becomes $12 (4 y^{2} + y - 3)$

03

Step 3. Compare the trinomial with ax2+bx+c

Compare $a x^{2} + b x + c$ with $4 y^{2} + y - 3$

So $a = 4$ , $b = 1$ and $c = - 3$

Find product of a and c

$a c = - 12$

04

Step 4. Factor of ac

Find two numbers such as product is $- 12$ and sum is 1.

So, 4 and -3

05

Step 5. Find factors

Rewrite trinomial $12 (4 y^{2} + y - 3)$

$12 (4 y^{2} + 4 y - 3 y - 3)$

Factor the trinomial

role="math" localid="1644516977880" $12 (4 y (y + 1) - 3 (y + 1)) 12 (y + 1) (4 y - 3)$

06

Step 6. Check

Multiply $12 (y + 1) (4 y - 3)$

$12 (4 y^{2} + y - 3) 48 y^{2} + 12 y - 36$

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Most popular questions from this chapter

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