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: 91



Work Step by Step

The two numbers whose product is $ac= 4(49)=196 $ and whose sum is $b= 28 $ are $\{ 14,14 \}$. Using these two numbers to decompose the middle term of the expression, $ 4z^2+28z+49 ,$ then the factored form is \begin{array}{l}\require{cancel} 4z^2+14z+14z+49 \\\\= (4z^2+14z)+(14z+49) \\\\= 2z(2z+7)+7(2z+7) \\\\= (2z+7)(2z+7) \\\\= (2z+7)^2 .\end{array}
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