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: 29

Answer

$(n+2)(n-5)$

Work Step by Step

To factor a trinomial in the form $n^2+bn+c$, 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 $(n+\_)(n+\_)$. In the case of $n^2-3n-10$, we are looking for two numbers whose product is $-10$ and whose sum is $-3$. The numbers $2$ and $-5$ meet these criteria because: $$2\times(-5)=-10\;\text{and}\;2+(-5)=-3$$When we insert these numbers into the blanks, we arrive at the factors: $(n+2)(n-5)$.
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