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: 74

Answer

number to be added: $49$ factored form: $(p+7)^2$

Work Step by Step

RECALL: To complete the square for 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 $(\frac{14}{2})^2=7^2=49$ to obtain: $p^2 + 14p + 49$ Writing the square in factored form gives: $p^2+14p+49 = (p+7)^2$
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