Question 93560
For this problem you can tell this rather quickly. By looking at this problem you can tell
that only one of two factors can be squared to give you the trinomial. Either it is:
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{{{(x-4)^2}}}
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or it is:
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{{{(x+4)^2}}}
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[You can tell this is the case because if the trinomial is a perfect square, its factor
must involve the square root of its first term and the square root of its last term. So
it must involve the square root of {{{x^2}}} which is x and it must also involve the square
root of its last term ... the square root of 16 which is 4.]
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But notice something ... in either of these cases [the cases involving (x - 4) and (x + 4)]
when you square the last terms ... square -4 or square +4, the result is +16. But the
trinomial contains -16 as the last factor. So it can't be a perfect square.
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From this analysis you learn one general thing. That to be a perfect square, a trinomial must 
have plus signs on its first and last terms. 
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Hope this helps you to understand more than just the answer you needed.