College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.4 - Factoring Polynomials - R.4 Exercises - Page 40: 82

Answer

$(10x+17)^2$

Work Step by Step

Let $z=5x+7.$ Then the given expression, $ 4(5x+7)^2+12(5x+7)+9 ,$ is equivalent to \begin{array}{l}\require{cancel} 4z^2+12z+9 .\end{array} The two numbers whose product is $ac= 4(9)=36 $ and whose sum is $b= 12 $ are $\{ 6,6 \}.$ Using these two numbers to decompose the middle term, then the factored form of $ 4z^2+12z+9 $ is \begin{array}{l}\require{cancel} 4z^2+6z+6z+9 \\\\= (4z^2+6z)+(6z+9) \\\\= 2z(2z+3)+3(2z+3) \\\\= (2z+3)(2z+3) \\\\= (2z+3)^2 .\end{array} Since $z=5x+7$, then the expression $ (2z+3)^2 $ is equivalent to \begin{array}{l}\require{cancel} (2(5x+7)+3)^2 \\\\= (10x+14+3)^2 \\\\= (10x+17)^2 .\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.