標題:
F.3 Factorization
發問:
a) Factorize x^3 + 27. b) Factorize 5x^2 - 2x - 51 . c) Using the result of (a) and (b), factorize x^3 + 5x^2 -2x - 24 .
最佳解答:
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a) a^3 + b^3 = (a+b)[(a^2) -a*b + (b^2)] x^3 + 27 = (x + 3)(x^2 - 3x + 9) b) 5x^2 - 2x - 51 = (5x - 17)(x + 3) c) x^3 + 5x^2 -2x - 24 = (x^3 + 27) + (5x^2 - 2x - 51) = (x + 3)(x^2 - 3x + 9) + (5x - 17)(x + 3) = (x + 3) [(x^2 - 3x + 9) + (5x - 17)] = (x + 3)(x^2 + 2x - 8) = (x + 3)(x + 4)(x - 2)
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