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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. 138E (page 590)

In the following exercises, factor each expression using any method $q^{2} - 29 q r - 96 r^{2}$

Short Answer

Expert verified

The factor are $(q + 3 r) (q - 32 r)$

Step by step solution

01

Step 1. Given Information

The trinomial is $q^{2} - 29 q r - 96 r^{2}$

Find factors by splitting middle term

02

Step 2. Factor the trinomial

Split the middle term of trinomial to find factors

Find two numbers such as their product is $- 96$ and sum is $- 29$

The number are $- 32$ and $3$

$q^{2} + 3 q r - 32 q r - 96 r^{2} q (q + 3 r) - 32 r (q + 3 r) (q + 3 r) (q - 32 r)$

03

Step 3. Check

Multiply the factor $(q + 3 r) (q - 32 r)$

$q^{2} + 3 q r - 32 q r - 96 r^{2} q^{2} - 29 q r - 96 r^{2}$

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Most popular questions from this chapter

Factor completely using trial and error: $10 y^{2} - 37 y + 7$

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