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: 27

Answer

$(x+6)(x-1)$

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 $x^2+5x-6$, we are looking for two numbers whose product is $-6$ and whose sum is $5$. The numbers $6$ and $-1$ meet these criteria because: $$6\times(-1)=-6\;\text{and}\;6+(-1)=5$$When we insert these numbers into the blanks, we arrive at the factors: $(x+6)(x-1)$.
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