Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Section 5.2 - Factoring Trinomials - 5.2 Exercises: 7

Answer

$(x+3)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ x^2+8x+15 ,$ find two numbers, $m_1$ and $m_2,$ whose product is $c$ and whose sum is $b$ in the quadratic expression $x^2+bx+c.$ Then, express the factored form as $(x+m_1)(x+m_2).$ $\bf{\text{Solution Details:}}$ In the given expression, the value of $c$ is $ 15 $ and the value of $b$ is $ 8 .$ The possible pairs of integers whose product is $c$ are \begin{array}{l}\require{cancel} \{ 1,15 \}, \{ 3,5 \}, \{ -1,-15 \}, \{ -3,-5 \} .\end{array} Among these pairs, the one that gives a sum of $b$ is $\{ 3,5 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} (x+3)(x+5) .\end{array} The missing factor in the given expression is $ (x+3) .$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.