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 - Chapter Review: 42

Answer

$(g-7)(g+2)$

Work Step by Step

To factor a trinomial in the form $g^2+bg+c$, 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 $(g+\_)(g+\_)$. In the case of $g^2-5g-14$, we are looking for two numbers whose product is $-14$ and whose sum is $-5$. The numbers $-7$ and $2$ meet these criteria because: $$-7\times(2)=-14\;\text{and}\;-7+(2)=-5$$When we insert these numbers into the blanks, we arrive at the factors: $(g-7)(g+2)$.
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