Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Exercise Set 6.5 - Page 399: 18



Work Step by Step

$x^{2}$ -9x +81 step 1. Enter x as the first term of each factor $x^{2}$ -9x +81= (x__)(x _) Step 2. To find the second term of each factor, we must find two integers whose product is 81 and whose sum is -9 List pairs of factors of the constant, 81 (1,81)(-1,-18)(3,27)(-3,-27))(9,9)(-9,-9) step 3. The correct factorization of $x^{2}$ -9x +81 is the one in which the sum of the Outside and Inside products is equal to -9x. Since there are no factors that can sum up to -9, this polynomial is prime.
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