SOLUTION: how do u factor x^3+64 and what are the roots of the polynomials?

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Question 245743: how do u factor x^3+64 and what are the roots of the polynomials?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3%2B64 Start with the given expression.


%28x%29%5E3%2B%284%29%5E3 Rewrite x%5E3 as %28x%29%5E3. Rewrite 64 as %284%29%5E3.


%28x%2B4%29%28%28x%29%5E2-%28x%29%284%29%2B%284%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%28x%2B4%29%28x%5E2-4x%2B16%29 Multiply

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Answer:

So x%5E3%2B64 factors to %28x%2B4%29%28x%5E2-4x%2B16%29.


In other words, x%5E3%2B64=%28x%2B4%29%28x%5E2-4x%2B16%29


So to find the roots of x%5E3%2B64, just find the roots of %28x%2B4%29%28x%5E2-4x%2B16%29. In other words, solve the equation:


%28x%2B4%29%28x%5E2-4x%2B16%29=0