分解因式:(1)-x^n+2+3x^n+1+2x^n-6x^n-1 (2)(x^2+3x+1)(x^2+3x-3)-5 (3)(x^2-7x+6)(x^2-x-6)+56
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分解因式:(1)-x^n+2+3x^n+1+2x^n-6x^n-1 (2)(x^2+3x+1)(x^2+3x-3)-5 (3)(x^2-7x+6)(x^2-x-6)+56
分解因式:(1)-x^n+2+3x^n+1+2x^n-6x^n-1 (2)(x^2+3x+1)(x^2+3x-3)-5 (3)(x^2-7x+6)(x^2-x-6)+56
分解因式:(1)-x^n+2+3x^n+1+2x^n-6x^n-1 (2)(x^2+3x+1)(x^2+3x-3)-5 (3)(x^2-7x+6)(x^2-x-6)+56
(1)-x^(n+2)+3x^(n+1)+2x^n-6x^(n-1)
=-x^(n-1)(x^3-3x^2-2x+6)
=-x^(n-1)[(x^3-3x^2)-(2x-6)]
=-x^(n-1)[x^2(x-3)-2(x-3)]
=-x^(n-1)(x-3)(x^2-2)
(2)(x^2+3x+1)(x^2+3x-3)-5
=(x^2+3x)^2-2(x^2+3x)-3-5
=(x^2+3x)^2-2(x^2+3x)-8
=(x^2+3x-4)(x^2+3x+2)
=(x+4)(x-1)(x+1)(x+2)
(3)(x^2-7x+6)(x^2-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56
=[(x-1)(x-3)][(x-6)(x+2])+56
=(x^2-4x+3)(x^2-4x-12)+56
=(x^2-4x)^2-9(x^2-4x)-36+56
=(x^2-4x)^2-9(x^2-4x)+20
=(x^2-4x-4)(x^2-4x-5)
=(x^2-4x-4)(x-5)(x+1)
(1)-x^n+2+3x^n+1+2x^n-6x^n-1
=﹣(x^n+2-3x^n+1)+(2x^n-6x^n-1)
=﹣x^n+1(x-3)+2x^n-1(x-3)
=x^n-1(x-3)(2-x²)
=x^n-1(x-3)(√2+x)(√2-x)
(2)(x^2+3x+1)(x^2+3x-3)-5
=(x²+3x)²...
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(1)-x^n+2+3x^n+1+2x^n-6x^n-1
=﹣(x^n+2-3x^n+1)+(2x^n-6x^n-1)
=﹣x^n+1(x-3)+2x^n-1(x-3)
=x^n-1(x-3)(2-x²)
=x^n-1(x-3)(√2+x)(√2-x)
(2)(x^2+3x+1)(x^2+3x-3)-5
=(x²+3x)²-2(x²+3x)-3-5
=(x²+3x)²-2(x²+3x)-8
=(x²+3x-4)(x²+3x+2)
=(x+4)(x-1)(x+1)(x+2)
(3)(x^2-7x+6)(x^2-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56
=[(x-1)(x-3)][(x-6)(x+2)]+56
=(x²-4x+3)(x²-4x-12)+56
=(x²-4x)²-9(x²-4x)+20
=(x²-4x-4)(x²-4x-5)
=(x²-4x-4)(x-5)(x+1)
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