初中因式分解 (x2+3x+2)*(x2+7x+12)-120

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初中因式分解 (x2+3x+2)*(x2+7x+12)-120

初中因式分解 (x2+3x+2)*(x2+7x+12)-120
初中因式分解 (x2+3x+2)*(x2+7x+12)-120

初中因式分解 (x2+3x+2)*(x2+7x+12)-120
(X2+3X+2)(X2+7X+12)-120
=[x^2+(2+1)x+1*2][x^2+(3+4)x+3*4]-120
=(x+1)(x+2)(x+3)(x+4)-120
=[(x+2)(x+3)][(x+1)(x+4)]-120
=(x^2+5x+6)(x^2+5x+4)-120
=(x^2+5x)^2+10(x^2+5x)+24-120
=(x^2+5x)^2+10(x^2+5x)-96
=(x^2+5x)^2+[16+(-6)](x^2+5x)+(16)*(-6)
=(x^2+5x-6)(x^2+5x+16)
=(x-1)(x+6)(x^2+5x+16)

=(x+1)(x+2)(x+3)(x+4)-120
=(x²+5x+4)(x²+5x+6)-120
=(x²+5x)²+10(x²+5x)-96
=(x²+5x+16)(x²+5x-6)
=(x²+5x+16)(x+6)(x-1)

(x+i)(x+2)(x+3)(x+4)-120