Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-5 Factoring x2+bx+c - Lesson Check: 2

Answer

$(r-6)(r-7)$

Work Step by Step

To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$. In the case of $r^2-13r+42$, we are looking for two numbers whose product is $42$ and whose sum is $-13$. The numbers $-6$ and $-7$ meet these criteria, because $$-6\times(-7)=42\;\text{and}\;-6+(-7)=-13$$When we insert these numbers into the blanks, we arrive at the factors: $(r-6)(r-7)$.
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