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: 5

Answer

$(x-2)(x+12)$

Work Step by Step

In order to factor $x^{2}+10x-24$, we must find a pair of numbers whose product is equal to -24 (or the constant term) and whose sum is equal to 10 (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 -24 are -1,24, 1,-24, -2,12, 2,-12, -3,8, 3,-8, -4,6, and 4,-6. Out of these pairs, the sum of -2 and 12 is equal to 10. Therefore, $x^{2}+10x-24=(x-2)(x+12)$.
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