SOLUTION: what is the step by step process of solving this polynomial by factoring? 27x^3+125=0

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Question 393464: what is the step by step process of solving this polynomial by factoring?
27x^3+125=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Facor:
27x%5E3%2B125+=+0 Did you notice that you have the sum of two cubes?
%283x%29%5E3%2B%285%29%5E3+=+0
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 = 3x and B = 5, so...
27x%5E3%2B125+=+0 becomes:
%283x%2B5%29%289x%5E2-15x%2B25%29+=+0 Apply the zero product rule:
3x%2B5+=+0 or 9x%5E2-15x%2B25+=+0
Do the first factor:
3x%2B5+=+0 Subtract 5.
3x+=+-5 Divide by 3.
x%5B1%5D+=+-5%2F3
Do the second factor:
9x%5E2-15x%2B25+=+0 Use the quadratic formula to solve: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a and a = 9, b = -15, and c = 25.
x+=+%28-%28-15%29%2B-sqrt%28%28-15%29%5E2-4%289%29%2825%29%29%29%2F2%289%29
x+=+%2815%2B-sqrt%28225-900%29%29%2F18
x+=+%2815%2B-sqrt%28-675%29%29%2F18 and when you work this out, you should get:
x%5B2%5D+=+0.833%2B1.44i and x%5B3%5D+=+0.833-1.44i