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 - Page 57: 77


number to be added: $\dfrac{1}{16}$ factored form: $(x-\frac{1}{4})^2$

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 $(\dfrac{\frac{1}{2}}{2})^2=(\frac{1}{4})^2=\frac{1}{16}$ to obtain: $x^2 -\frac{1}{2}x + \frac{1}{16}$ Writing the square in factored form gives: $x^2-\frac{1}{4}x+\frac{1}{16} = (x-\frac{1}{4})^2$
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