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Q15.

Expert-verified

Algebra 1

Found in: Page 492

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

Factor each polynomial.
$5 a^{2} - 25 a - a + 5$

The factors of given polynomial are $(5 a - 1) (a - 5)$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Combine.

Combine like terms in the given polynomial.

$5 a^{2} - 26 a + 5$

Step 2. Find the GCF.

Find the GCF of $5 a^{2}, 26 a$ and 5.

$5 a^{2} = 1 \cdot 5 \cdot a \cdot a 26 a = 1 \cdot 2 \cdot 13 \cdot a 5 = 1 \cdot 5$

Therefore, GCF is 1.

Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of 25 and sum of $- 26$ . The numbers are $- 1$ and $- 25$ .

$5 a^{2} + m x + n x + 5 = 5 a^{2} - 25 a - 1 a + 5$

Step 4. Group terms with common factors and factor out GCF.

Group terms with common factors and factor out GCF from each grouping.

$(5 a^{2} - 25 a) + (- 1 a + 5) = 5 a (a - 5) - 1 (a - 5) = (5 a - 1) (a - 5)$

Therefore, the factors of $5 a^{2} - 25 a - a + 5$ are $(5 a - 1) (a - 5)$ .

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