Question

因式分解：（x²+1)²-x²+x(x-2)(x²+x+1)

Answer 1

原式=x^4+x²+1+x(x-1)(x²+x+1)-x(x²+x+1)

=x(x-1)(x²+x+1)+x^4-x³-x+1

=x(x-1)(x²+x+1)+x³(x-1)-(x-1)

=(x-1)[x(x²+x+1)+(x-1)(x²+x+1)]

=(x-1)(x²+x+1)(2x-1)

解法2

原式=(x²+1+x)(x²+1-x)+x(x-2)(x²+x+1)

=(x²+x+1)(x²+1-x+x²-2x)

=(x²+x+1)(2x²-3x+1)

=(x²+x+1)(x-1)(2x-1)