Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - 8.1 Exercises - Page 512: 48

Answer

Third Term: $\dfrac{9}{4}$ Factored Form: $\left(t+\dfrac{3}{2}\right)^2$

Work Step by Step

The third term, $c,$ of a perfect square trinomial is equal to the square of half the coefficient of the second term, $b$. That is, \begin{align*} c=\left(\dfrac{b}{2}\right)^2 .\end{align*} Thus, in the given incomplete expression, $ t^2+3t+\overset{?}\_ $, the missing third term, $c,$ that will make the trinomial a perfect square is \begin{align*} c&=\left(\dfrac{b}{2}\right)^2 \\\\&= \left(\dfrac{3}{2}\right)^2 \\\\&= \dfrac{9}{4} .\end{align*} Taking the square roots of the first and second terms and following the sign of the middle term, the factored form of $ t^2+3t+\dfrac{9}{4} ,$ is $\left(t+\dfrac{3}{2}\right)^2$.
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