Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 11

Answer

$4z(x+2)(x+5)$

Work Step by Step

In order to factor $4x^{2}z+28xz+40z$, we must first factor out a 4z (which is the greatest common factor of each term) from all three terms. $4z(x^{2}+7x+10)$ Next, we must find a pair of numbers whose product is equal to 10 (or the constant term) and whose sum is equal to 7 (or the coefficient on the middle term). We know that the pairs of numbers whose product is 10 are 1,10 and 2,5. Out of these pairs, the sum of 2 and 5 is equal to 7. Therefore, $4x^{2}z+28xz+40z=4z(x+2)(x+5)$.
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