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Q. 104

Expert-verified

Elementary Algebra

Found in: Page 832

Book edition 2nd

Author(s) Lynn Marecek, MaryAnne Anthony-Smith

Pages 1240 pages

ISBN 9780998625713

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Short Answer

In the following exercises, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$p^{2} - 8 p q - 65 q^{2}$

The factorization of $p^{2} - 8 p q - 65 q^{2}$ is $(p + 5 q) (p - 13 q)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

Given expression is $p^{2} - 8 p q - 65 q^{2}$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

The factor of -65	Sum of factor
5, -13	5 + (-13) = -8

13, -5

13 +(-5) = 8

Step 3. factorization

Use $5$ and $- 13$ as the last terms of the trinomials.

$p^{2} - 8 p q - 65 q^{2} = (p + 5 q) (p - 13 q)$

Step 4. Check

$(p + 5 q) (p - 13 q) = p^{2} + 5 p q - 13 p q - 65 q^{2} = p^{2} - 8 p q - 65 q^{2}$

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