SOLUTION: can you please help me solve this polynomial equation (x^3+8) by factoring and using the principle of zero products? i've been having a lot of problems with this one and its confus

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can you please help me solve this polynomial equation (x^3+8) by factoring and using the principle of zero products? i've been having a lot of problems with this one and its confus      Log On


   

Question 497313: can you please help me solve this polynomial equation (x^3+8) by factoring and using the principle of zero products? i've been having a lot of problems with this one and its confusing me. thank you in advance
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
can you please help me solve this polynomial equation (x^3+8) by factoring and using the principle of zero products?
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Solve: x^3+8 = 0
Factor:
(x+2)(x^2-2x+4) = 0
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x = -2 and
Solve x^2-2x+4 = 0
x = [2 +- sqrt(4-4*4)]/2
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x = [2 +- sqrt(-12)]/2
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x = [2 +- 2sqrt(3)i]/2
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x = 1+sqrt(3)i or x = 1-sqrt(3)i
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Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by factoring:
%28x%5E3%2B8%29 Can't really solve this "expression" until you set it equal to something, thus making it an "equation", but we can factor it.
x%5E3%2B8+=+%28x%29%5E3%2B%282%29%5E3 so we have the sum of cubes and there is a factored form for this:
A%5E3%2BB%5E3+=+%28A%2BB%29%28A%5E2-AB%2BB%5E2%29 so...
%28x%29%5E3%2B%282%29%5E3+=+%28x%2B2%29%28x%5E2-2x%2B4%29...and that's the best we can do!