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: 10

Answer

$5(x-2)(x-7)$

Work Step by Step

In order to factor $5x^{2}-45x+70$, we must first factor out a 5 (which is the greatest common factor of each term) from all three terms. $5(x^{2}-9x+14)$ Next, we must find a pair of negative numbers whose product is equal to 14 (or the constant term) and whose sum is equal to -9 (or the coefficient on the middle term). We know that the pairs of negative numbers whose product is 14 are -1,-14 and -2,-7. Out of these pairs, the sum of -2 and -7 is equal to -9. Therefore, $5x^{2}-45x+70=5(x-2)(x-7)$.
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