因式分解：(x-1)(x-2)x(x+1)+1 (x^2+2x)(x^2+2x-2)-3 全要过程

Question

因式分解：(x-1)(x-2)x(x+1)+1
(x^2+2x)(x^2+2x-2)-3
全要过程
全都要写过程

Answer 1

(x-1)(x-2)x(x+1)+1
=(x-2)(x+1)x(x-1)+1
=(x²-x-2)(x²-x)+1
=(x²-x)²-2(x²-x)+1
=(x²-x-1)²

(x^2+2x)(x^2+2x-2)-3
=(x²+2x)²-2(x²+2x)-3
=(x²+2x-3)(x²+2x+1)
=(x+3)(x-1)(x+1)²本回答被提问者采纳

Answer 2

分解因式：
(x-1)(x-2)x(x+1)+1
=(x-2)(x+1)x(x-1)+1
=(x²-x-2)(x²-x)+1
=(x²-x)²-2(x²-x)+1
=(x²-x-1)²

(x^2+2x)(x^2+2x-2)-3
=(x²+2x)²-2(x²+2x)-3
=(x²+2x-3)(x²+2x+1)
=(x+3)(x-1)(x+1)²

Answer 3

(x-1)(x-2)x(x+1)+1(x^2+2x)(x^2+2x-2)-3
=(x-1)(x-2)x(x+1)+1(x^2+2x)(x^2+2x-2)-3
=x[(x^2-1)(x-2)+(x+2)(x^2+2x-2)]-3
=x(x^3-x-2x^2+2+x^3+2x^2-2x+2x^2+4x-4)-3
=x(2x^3+2x^2+x-2)-3
=2x^4+2x^3+x^2-2x-3
=2x^3(x+1)+(x+1)(x-3)
=(x+1)(2x^3+x-3)
=(x+1)[(2x^3-2)+(x-1)]
=(x+1)[2(x-1)(x^2+x+1)+(x-1)]
=(x+1)(x-1)(2x^2+2x+2+1)
=(x+1)(x-1)(2x^2+2x+3)

Answer 4

。。。。。。。。。。。。