College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.5 - Factoring Polynomials - R.5 Assess Your Understanding: 78

Answer

number to be added: $\dfrac{1}{36}$ factored form: $(x+\frac{1}{6})^2$

Work Step by Step

RECALL: To complete the square of an expression in the form $x^2+bx$, $(\frac{b}{a})^2$ must be added. The factored form of the result is $(x+\frac{b}{2})^2$. Thus, in the given expression add $(\dfrac{\frac{1}{3}}{2})^2=(\frac{1}{6})^2=\frac{1}{36}$ to obtain: $x^2 +\frac{1}{3}x + \frac{1}{36}$ Writing the square in factored form gives: $x^2+\frac{1}{3}x+\frac{1}{36} = (x+\frac{1}{6})^2$
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