如何对这个多项式进行因式分解?-X^3+4X^2-5X+2请给出思路和解法,我分了半天,也没分出来,泪目～老师请教教我吧～～

Question

如何对这个多项式进行因式分解 ? -X^3 + 4X^2 -5X +2 请给出思路和解法,我分了半天,也没分出来,泪目～
老师请教教我吧～～

Answer 1

原式=-(x³-4x²+4x+x-2)
=-(x(x²-4x+4)+(x-2))
=-(x(x-2)²+(x-2)
=-(x-2)(x(x-2)+1)
=-(x-2)(x-1)²
原式=-(x³-4x²+3x+2x-2)
=-(x(x²-4x+3)+2(x-1))
=-(x(x-1)(x-3)+2(x-1))
=-(x-1)(x(x-3)+2)
=-(x-1)(x²-3x+2)
=-(x-1)(x-1)(x-2)
=-(x-1)²(x-2)