Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.3 Factoring Trinomials of the Type ax2+bx+c - 5.3 Exercise Set: 39

Answer

$(x+1)(3x+1)$

Work Step by Step

Rearranging the terms, the given expression is equivalent to \begin{array}{l}\require{cancel} 4x+1+3x^2 \\\\= 3x^2+4x+1 .\end{array} Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} 3x^2+4x+1 \end{array} has $ac= 3(1)=3 $ and $b= 4 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 3,1 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 3x^2+3x+1x+1 .\end{array} Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} (3x^2+3x)+(x+1) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 3x(x+1)+(x+1) .\end{array} Factoring the $GCF= (x+1) $ of the entire expression above results to \begin{array}{l}\require{cancel} (x+1)(3x+1) .\end{array}
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.