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: 81

Answer

$(3a-7)^2$

Work Step by Step

Let $z=a-4.$ Then the given expression, $ 9(a-4)^2+30(a-4)+25 ,$ is equivalent to \begin{array}{l}\require{cancel} 9z^2+30z+25 .\end{array} The two numbers whose product is $ac= 9(25)=225 $ and whose sum is $b= 30 $ are $\{ 15,15 \}.$ Using these two numbers to decompose the middle term, then the factored form of $ 9z^2+30z+25 $ is \begin{array}{l}\require{cancel} 9z^2+15z+15z+25 \\\\= (9z^2+15z)+(15z+25) \\\\= 3z(3z+5)+5(3z+5) \\\\= (3z+5)(3z+5) \\\\= (3z+5)^2 .\end{array} Since $z=a-4$, then the expression $ (3z+5)^2 $ is equivalent to \begin{array}{l}\require{cancel} (3(a-4)+5)^2 \\\\= (3a-12+5)^2 \\\\= (3a-7)^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.