SOLUTION: factor 2x^3-128

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Question 168971: factor 2x^3-128
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E3-128 Start with the given expression


2%28x%5E3-64%29 Factor out the GCF 2


Now let's focus on the inner expression x%5E3-64


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x%5E3-64 Start with the inner expression.


%28x%29%5E3-%284%29%5E3 Rewrite x%5E3 as %28x%29%5E3. Rewrite 64 as %284%29%5E3.


%28x-4%29%28%28x%29%5E2%2B%28x%29%284%29%2B%284%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28x-4%29%28x%5E2%2B4x%2B16%29 Multiply


So x%5E3-64 factors to %28x-4%29%28x%5E2%2B4x%2B16%29.

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Answer:
So 2x%5E3-128 completely factors to 2%28x-4%29%28x%5E2%2B4x%2B16%29