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: 22

Answer

(5x+2)(5x+2)

Work Step by Step

$20x+25x^{2}+4=25x^{2}+20x+4$ First, identify two numbers that multiply with each other to become 100, the product of the constant and coefficient of $x^{2}$ (4 $\times$ 25) and add together to become 20, the coefficient of x. From inspection, we identify the numbers as 10 and 10. Secondly split the coefficient of x into the sum of the two above numbers. $25x^{2}+20x+4$ $=25x^{2}+(10+10)x+4$ $=25x^{2}+10x+10x+4$ Factorize by grouping to find the answer. $25x^{2}+10x+10x+4$ $=5x(5x+2)+2(5x+2)$ $=(5x+2)(5x+2)$
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