SOLUTION: How do you factor x^3+8?

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Question 97039: How do you factor x^3+8?
Found 2 solutions by Earlsdon, mathslover:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
x%5E3%2B8 Do you recognise this as the sum of two cubes?
x%5E3%2B8+=+%28x%29%5E3%2B%282%29%5E3...but of course!
The sum of two cubes can be factored thus:
A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29
In your problem, A = x and B = 2, so...
x%5E3%2B8+=+%28x%2B2%29%28x%5E2-2x%2B4%29 and we're done!
Let's check the solution by multiplying the two factors, using FOIL.
%28x%2B2%29%28x%5E2-2x%2B4%29+=+x%5E3-2x%5E2%2B4x%2B2x%5E2-4x%2B8 Simplify by combining like-terms.
x%5E3%2B8+=+x%5E3%2B8

Answer by mathslover(157) About Me  (Show Source):
You can put this solution on YOUR website!

In general a^3 + b^3 = (a + b) (a^2 - ab + b^2)
the given expression x^3 + 8 can be written as
x^3 + 2^3
= (x + 2 )(x^2 - 2*x + 2^2)
= (x + 2 )(x^2 - 2x + 4)