SOLUTION: How do I factor 10x^2-160

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Question 897284: How do I factor
10x^2-160
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
First, look for common factors:
10x%5E2-160=10%28x%5E2-16%29 .
Next, see if you have a "special product, such as a perfect square, or a difference of squares.
Here you have a difference of squares:
10%28x%5E2-16%29=10%28x%5E2-4%5E2%29=highlight%2810%28x%2B4%29%28x-4%29%29 .

If you did not recognize a special product, you would try to find factors
that multiply to give you x%5E2-16 .
You know that it would be something like
%28x%2Ba%29%28x%2Bb%29 , with two numbners a and b that you have to find.
Since %28x%2Ba%29%28x%2Bb%29=x%5E2%2Bbx%2Bax%2Bab=x%5E2%2B%28a%2Bb%29x%2Bab ,
and that has to equal x%5E2-16 ,
you are looking for numbers that make the coefficients the same.
It must be a%2Bb=0 and ab=-16 .
To make ab=-16 the numbers for a and b muat be
either -1 and 16,
or 1 and-16,
or -1 and 8,
or 2 and -8,
or -4 and 4.
The only pair that adds up to 0 is -4 and 4, so
x%5E2-16=%28x-4%29%28x%2B4%29