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anonymous
 5 years ago
how do you factor cubes? ex. x^3+216 ex. x^31
anonymous
 5 years ago
how do you factor cubes? ex. x^3+216 ex. x^31

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Recognize that 216 = 6^3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Then\[x^3+216=x^3+6^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can split off a factor of (x+6) now.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can use polynomial division, or any other method that works (there are a few).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I do this...take the factor and write it out as many times as the highest power, like (x+6) (x+6) (x+6) leaving spaces. Then I ask myself, "What do I need to multiply the first one by in order to get x^3?" The answer is x^2. So I write, x^2(x+6) (x+6) (x+6) Next, when I mentally expand that first factor, I'll get x^3 +3x^2. I don't want 6x^2, so looking at the next factor I ask, "What do I have to multiply the second factor by to get rid of the 6x^2?" Well, x^2(x+6) 6x(x+6) (x+6) Now when I mentally expand the second bracket, I get 6x^2 (good) but now also, 36x. I look to the last factor and ask, "What do I have to multiply this one by in order to get rid of the 36x?" Well, multiply it by 36. Then, x^2(x+6)  6x(x+6) + 36(x+6) Now when I expand the last one mentally, I get 36x (good) and 216 (good again). The common factor of (x+6) can be taken out from above to give, \[(x+6)(x^26x+36)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can't factorize any further unless you use complex numbers.
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