SOLUTION: factor {{{x^3+3x^2-8x-24}}}

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Question 610924: factor x%5E3%2B3x%5E2-8x-24
Found 2 solutions by solver91311, radh:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Rearrange



Factor from the first two terms and factor 3 from the last two terms:



Note the common binomial factor, factor it out:



Now, depending on whether you are required to factor over the rationals (if so, you are done) or over the reals (if so, continue)



looks very much like the difference of two squares, except that 8 isn't a square. Or is it...?



So:



And your complete factorization, over the reals, is:



John

My calculator said it, I believe it, that settles it
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Answer by radh(108) About Me  (Show Source):
You can put this solution on YOUR website!
First, group the first two terms together, and the second two terms together.
%28x%5E3%2B3x%5E2%29%2B%28-8x-24%29
Then, we find the GCF of each group.
%28x%5E2%28x%2B3%29-8%28x%2B3%29%29
Since both groups contain the same GCF, they can be combined into:
%28x%5E2-8%29%28x%2B3%29. There's your answer! :)