Is the following trinomial a perfect square?
x^2+8x-16
Thank you Found 2 solutions by Edwin McCravy, bucky:Answer by Edwin McCravy(20054) (Show Source):
Is the following trinomial a perfect square?
x^2+8x-16
Thank you
How to test a trinomial to see if it is a perfect square:
1. Find square roots of first and last terms.
2. Multiply them together.
3. Double what you have so far.
4. Do you get the middle term or the middle term with the opposite sign?
If so the trinomial is a perfect square.
Oh,oh, last term is negative and I can't get the square root of it.
So no, it's not a perfect square.
If it had been or it would have been,
but if the last sign is negative, it never can be a perfect square.
The last term must be positive.
Edwin
You can put this solution on YOUR website! 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:
.
.
or it is:
.
.
[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 which is x and it must also involve the square
root of its last term ... the square root of 16 which is 4.]
.
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.
.
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.
.
Hope this helps you to understand more than just the answer you needed.
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