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如何化简x(4次方)-2x(3次方)-7x(2次方)8x12
题目详情
如何化简x(4次方)-2x(3次方)-7x(2次方) 8x 12
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答案和解析
x(4次方)-2x(3次方)-7x(2次方)+ 8x+12
=x^4+x^3-3x^3-3x^2-4x^2-4x+12x+12
=(x^4+x^3)+(-3x^3-3x^2)+(-4x^2-4x)+(12x+12)
=x^3(x+1)-3x^2(x+1)-4x(x+1)+12(x+1)
=(x+1)(x^3-3x^2-4x+12)
=(x+1)[(x^3-3x^2)+(-4x+12)]
=(x+1)[x^2(x-3)-4(x-3)]
=(x+1)(x-3)(x^2-4)
=(x+1)(x-2)(x+2)(x-3)
=x^4+x^3-3x^3-3x^2-4x^2-4x+12x+12
=(x^4+x^3)+(-3x^3-3x^2)+(-4x^2-4x)+(12x+12)
=x^3(x+1)-3x^2(x+1)-4x(x+1)+12(x+1)
=(x+1)(x^3-3x^2-4x+12)
=(x+1)[(x^3-3x^2)+(-4x+12)]
=(x+1)[x^2(x-3)-4(x-3)]
=(x+1)(x-3)(x^2-4)
=(x+1)(x-2)(x+2)(x-3)
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