SOLUTION: Factor t^2+4t+4

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Question 1066952: Factor t^2+4t+4
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+t%5E2+%2B+4t+%2B+4+
There are different ways to factor it, but if
you use the quadratic formula, that will
tell you things about the function that
you wouldn't learn otherwise.
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
The +- in the formula tells you this is really
2 formulas in one. They are:
+t%5B1%5D+=+%28+-b+%2B+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
and
+t%5B2%5D+=+%28+-b+-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+t%5B1%5D+ and +t%5B2%5D+ are the roots
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Notice that if +b%5E2+-+4%2Aa%2Ac+=+0+, then
there is only 1 root. It is called a double root
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In this case:
+a+=+1+
+b+=+4+
+c+=+4+
+b%5E2+-+4%2Aa%2Ac+=+4%5E2+-+4%2A1%2A4+
+b%5E2+-+4%2Aa%2Ac+=+0+
So you know you have only 1 root
----------------------------------------
Filling in the rest of the formula:
+t+=+%28+-b+%2B-+sqrt%28+0+%29%29+%2F+%282%2Aa%29+
+t+=+%28+-4+%2B-+sqrt%28+0+%29%29+%2F+%282%2A1%29+
+t+=+%28+-4+%29+%2F+2+
+t+=+-2+
That tells me the factors are:
+t+%2B+2+ repeated twice
so, it is factorized as:
+%28+t+%2B+2+%29%5E2+
Here's the plot. The double root, +t+=+-2+ is where the
curve just touches the x-axis
+graph%28+400%2C+400%2C+-10%2C+4%2C+-2%2C+10%2C+x%5E2+%2B+4x+%2B+4+%29+

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Recognize a perfect square trinomial whenever presented, especially for common ones.

t%5E2%2B4t%2B4=%28t%2B2%29%5E2