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 - Lesson Check: 1

Answer

$(x+3)(x+4)$

Work Step by Step

To factor a trinomial in the form $x^2+bx+c$, 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 $(x+\_)(x+\_)$. In the case of $x^2+7x+12$, we are looking for two numbers whose product is $12$ and whose sum is $7$. The numbers $3$ and $4$ meet these criteria, because $$3\times4=12\;\text{and}\;3+4=7$$When we insert these numbers into the blanks, we arrive at the factors: $(x+3)(x+4)$.
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