Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 6 - Section 6.4 - Factoring Trinomials of the Form ax2+bx+c by Grouping - Exercise Set: 25

Answer

$(2x-3)(5x-4)$

Work Step by Step

$10x^{2}−23x+12$ First, identify two numbers that multiply with each other to become 120, the product of the constant and coefficient of x2 (10 × 12) and add together to become -23, the coefficient of x. From inspection, we identify these numbers as -15 and -8. Secondly split the coefficient of x into the sum of the two above numbers. $10x^{2}−23x+12$ $=10x^{2}+(-15-8)x+12$ $=10x^{2}−15x-8x+12$ Factorize by grouping to find the answer. $10x^{2}−15x-8x+12$ $=5x(2x-3)-4(2x-3)$ $=(2x-3)(5x-4)$
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