Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises: 124

Answer

$c=25$

Work Step by Step

RECALL: There are two forms of perfect square trinomials: (1) $m^2+2mn+n^2$, which is the square of $(m+n)^2$; and (2) $m^2-2mn+n^2$, which is the square of $(m-n)^2$ The given trinomial has: $m^2 = 49x^2=(7x)^2$, which means that $m=7x$ The middle term of the trinomial is positive therefore the perfect square trinomial will be in the same form as in (1) above. Thus, $2mn=70x$ Since $m=7x$, substitute $m$ with $7x$ to obtain: $2mn=70x \\-2(7x)(n) = 70x \\-14x(n) = 70x$ Divide both sides by $-14x$ to obtain: $\dfrac{-14x(n)}{-14x} = \dfrac{70x}{-14x} \\n=-5$ The given trinomial is in the form $m^2+2mn+n^2$. Square $n$ to obtain: $n^2 = (-5)^2 = 25$ Therefore, the perfect square trinomial is $49x^2+70x+25$. Hence, $c=25$
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