因式分解(X+1)(X+2)(X+3)-6*7*8

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因式分解(X+1)(X+2)(X+3)-6*7*8
因式分解(X+1)(X+2)(X+3)-6*7*8

因式分解(X+1)(X+2)(X+3)-6*7*8
原式=[x+2-1](x+2)[x+2+1]-(7-1)7(7+1)
=(x+2)^3-(x+2)-(7^3-1)
=(x+2-7)[(x+2)^2+7(x+2)+49]-(x+2-7)
=(x-5)(x^2+11x+66)

(x+1)(x+2)(x+3)-6*7*8
设A=x+2
(A-1)A(A+1)-6*7*8
=(A^3-A)-(7^3-7)
=(A^3-7^3)-(A-7)
=(A-7)(A^2+7A+49-1)
=(x-5)[(x+2)^2+7(x+2)+48]
=(x-5)(x^2+11x+66)

x^3+6x^2+11x-330