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: 26

Answer

$(z-2)(z+4)$

Work Step by Step

To factor a trinomial in the form $z^2+bz+c$, 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 $(z+\_)(z+\_)$. In the case of $z^2+2z-8$, we are looking for two numbers whose product is $-8$ and whose sum is $2$. The numbers $-2$ and $4$ meet these criteria because: $$4\times(-2)=-8\;\text{and}\;4+(-2)=2$$When we insert these numbers into the blanks, we arrive at the factors: $(z-2)(z+4)$.
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