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From: Derek To: Teacher2Teacher Public Discussion Date: 2009091019:53:56 Subject: Re: Factoring the sum and difference of two cubes A great way to motivate this is to use synthetic division. For example: x^3-8=0 must have a zero of 2. When we synthetically divide by 2, we get 1 2 4, so x^3-8=(x-2)(x^2+x+4). Doing a couple more examples should make the pattern clear. It can also be generalized by synthetically dividing x^3-a^3 by a (one of its zeros).
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