SOLUTION: Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x6+24.

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Question 202825: Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x6+24.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E6%2B24 Start with the given expression.


3%28x%5E6%2B8%29 Factor out the GCF 3


3%28%28x%5E2%29%5E3%2B%282%29%5E3%29 Rewrite x%5E6 as %28x%5E2%29%5E3. Rewrite 8 as %282%29%5E3.


3%28x%5E2%2B2%29%28%28x%5E2%29%5E2-%28x%5E2%29%282%29%2B%282%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


3%28x%5E2%2B2%29%28x%5E4-2x%5E2%2B4%29 Multiply


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Answer:

So 3x%5E6%2B24 factors to 3%28x%5E2%2B2%29%28x%5E4-2x%5E2%2B4%29.


In other words, 3x%5E6%2B24=3%28x%5E2%2B2%29%28x%5E4-2x%5E2%2B4%29