Chapter 7: Q 124. (page 833)

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

Short Answer

Expert verified

The factorization of $q^{2} - 29 q r - 96 r^{2}$ is, $(q - 32 r) (q + 3 r)$ .

Step by step solution

Step 1. Given information

Given expression is $q^{2} - 29 q r - 96 r^{2}$ .

Step 2. Find the last terms of the trinomials

Write the factors as trinomials, $q$ in the first term of each binomial and $r$ in the second term.

localid="1649299564676" $(q_r) (q_r)$

Find the numbers that multiply to $- 96$ and add to $- 29$ .

Factors of -96	Sum of factors
-1, 96	-1 + 96 = 95
-2, 48	-2 + 48 = 46
-3, 32	-3 + 32 = 29
-4, 24	-4 + 24 = 20
-6, 10	-6 + 10 = 4
-8, 19	-8 + 19 = 11
-96, 1	-96 + 1 = -95
-48, 2	-48 + 2 = -46
-32, 3	-32 + 3 = -29*
-24, 4	-24 + 4 = 20
-10, 6	-10 + 6 = -4
-19, 8	-19 + 8 = -11

Step 3. Factorization

Use $- 32$ and $3$ as the last terms of the coefficents.

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

Step 4. Check

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

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials

Step 3. Factorization

Step 4. Check

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In the following exercises, factor each expression. q2-29qr-96r2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

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