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: 23

Answer

$(2x-7)(2x+3)$

Work Step by Step

$4x^{2}-8x-21$ First, identify two numbers that multiply with each other to become -84, the product of the constant and coefficient of $x^{2}$ (4 $\times$ -21) and add together to become -8, the coefficient of x. From inspection, we identify the numbers as 6 and -14. Secondly split the coefficient of x into the sum of the two above numbers. $4x^{2}-8x-21$ $=4x^{2}+(6-14)x-21$ $=4x^{2}+6x-14x-21$ Factorize by grouping to find the answer. $4x^{2}+6x-14x-21$ $=2x(2x+3)-7(2x+3)$ $=(2x-7)(2x+3)$
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