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: 52

Answer

$(w-18)(w+3)$

Work Step by Step

To factor a trinomial in the form $w^2+bw+c$, 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 $(w+\_)(w+\_)$. In the case of $w^2-15w-54$, we are looking for two numbers whose product is $-54$ and whose sum is $-15$. The numbers $-18$ and $3$ meet these criteria because: $$-18\times(3)=-54\;\text{and}\;-18+(3)=-15$$When we insert these numbers into the blanks, we arrive at the factors: $(w-18)(w+3)$.
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