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 - Practice and Problem-Solving Exercises: 24

Answer

$(r+9)(r-3)$

Work Step by Step

To factor a trinomial in the form $r^2+br+c$, 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 $(r+\_)(r+\_)$. In the case of $r^2+6r-27$, we are looking for two numbers whose product is $-27$ and whose sum is $6$. The numbers $9$ and $-3$ meet these criteria, because $$9\times(-3)=-27\;\text{and}\;9+(-3)=6$$When we insert these numbers into the blanks, we arrive at the factors $(r+9)(r-3)$.
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