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: 6

Answer

$(x-6)(x+9)$

Work Step by Step

In order to factor $x^{2}+3x-54$, we must find a pair of numbers whose product is equal to -54 (or the constant term) and whose sum is equal to 3 (or the coefficient on the middle term). We know that only a pair of one positive and one negative number will produce a negative product and a positive sum. We know that the pairs of numbers whose product is -54 are -1,54, 1,-54, -2,27, 2,-27, -3,18, 3,-18, -6,9, and 6,-9. Out of these pairs, the sum of -6 and 9 is equal to 3. Therefore, $x^{2}+3x-54=(x-6)(x+9)$.
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