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: 48

Answer

$(t-15)(t+2)$

Work Step by Step

To factor a trinomial in the form $t^2+bt+c$, 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 $(t+\_)(t+\_)$. In the case of $t^2-13t-30$, we are looking for two numbers whose product is $-30$ and whose sum is $-13$. The numbers $-15$ and $2$ meet these criteria because: $$-15\times(2)=-30\;\text{and}\;-15+(2)=-13$$When we insert these numbers into the blanks, we arrive at the factors: $(t-15)(t+2)$.
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