SOLUTION: Find the constant term to make x^2-4x a perfect square trinomial

Question 127519: Find the constant term to make x^2-4x a perfect square trinomial

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The process for this involves a just a couple of steps as follows:
.
First, make sure the multiplier of the x-squared term is 1. If it is different from 1 you have
to factor out that multiplier from both the x-squared term and the term containing x. In this
problem the multiplier of the x-squared term is 1, so we can skip this step.
.
Second, go to the term containing just the "x". Divide its multiplier by 2. Then square this
answer.
.
Third, add the squared answer to the terms you were given.
.
Let's apply these steps to the problem. You were given:
.

.
We can skip the first step as noted above. The second step tells you to take the -4, divide it
by 2 to get -2, and then square the -2 to get +4.
.
The third step tells you to add the plus 4 to what you were given. When you do that you have:
.

.
and that is a perfect square trinomial. It factors into:
.

.
and this is equal to
.
You can multiply out and you will find that the product is equal to
just as we made it.
.
Notice that the constant portion of the factors (the -2 in x - 2) comes from what you
got by dividing the -4 by 2 in step 2 because that's just the way this method works.
.
Hope this helps you to understand how to do problems of this type. Just remember the three steps.
.

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