SOLUTION: Divide x^2-4x+16 divided by x^3+64

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Question 373942: Divide
x^2-4x+16 divided by x^3+64
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E2-4x%2B16%29%2F%28x%5E3%2B64%29
There is a pattern for sum of cubes: a%5E3%2Bb%5E3+=+%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29. Since 64+=+4%5E3 the denominator fits this pattern. SO we can use the pattern to factor the denominator. With the numerators all we can do is factor out 1:

which simplifies as follows:
%281%2A%28x%5E2-4x%2B16%29%29%2F%28%28x%2B4%29%28x%5E2+-+4x+%2B+16%29%29

1%2F%28x%2B4%29