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Question 126433: Find the constant term that should be added to make the following expression a perfect-square trinomial.
x^2 – 4x
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The first thing to do is to check the x^2 term and make sure that its coefficient (multiplier)
is 1. In this problem it is, so you can proceed.
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Next look at the coefficient (multiplier) of the x term. That coefficient is -4. Then the
rule is to divide that by 2, square that, and add that result to the binomial you were originally
given. The result will be a perfect-square trinomial. Let's do it.
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Start with the multiplier of the x term. That multiplier is -4. Divide it by 2 and you get
an answer of -2. Square the -2 and you get +4. Add that to the original binomial you were
given and it becomes:
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x^2 - 4x + 4
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And this is the perfect-square trinomial you were to find.
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Notice that this can be factored as follows:
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x^2 - 4x + 4 = (x - 2)(x - 2) = (x-2)^2
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How can you easily tell what the factors will be? They will be x followed by half of the
original multiplier of the x term in the binomial ... in this case x followed by half of
the -4 that multiplied the x term. So the factors are both (x - 2).
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Hope this gives you some insight into the process of making a perfect-square trinomial
when you are given the first two terms that involve x^2 and x.
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