Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Concept and Vocabulary Check - Page 435: 3


Fill the blank with $10.$

Work Step by Step

With the foil method, with m and n being integers, we find that $(x+m)(x+n)=x^{2}+(m+n)x+ mn,$ so ,the sum of mn is the coefficient of x, and m and n are factors of the constant term. Reversing, when we want to factor $x^{2}+bx+c,$ we search for two integers, m and n such that their sum is b, their product is c. --- Here, we are given $b=13, c=30$ , and one of the integers is m=3. The other must be n=10, since $3\cdot 10=30,\quad 3+10=13.$
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