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: 9

Answer

$3(x-2)(x-4)$

Work Step by Step

In order to factor $3x^{2}-18x+24$, we must first factor out a 3 (which is the greatest common factor of each term) from all three terms. $3(x^{2}-6x+8)$ Next, we must find a pair of negative numbers whose product is equal to 8 (or the constant term) and whose sum is equal to -6 (or the coefficient on the middle term). We know that the pairs of negative numbers whose product is 8 are -1,-8 and -2,-4. Out of these pairs, the sum of -2 and -4 is equal to -6. Therefore, $3x^{2}-18x+24=3(x-2)(x-4)$.
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