因式分解(1)x^3-11x²+31x-21 (2) x^3-2x²+4

1个回答

  • (1)原式

    =(x³-1)-(11x³-31x+20)

    =(x-1)(x²+x+1)-(11x-20)(x-1)

    =(x-1)(x²+x+1-11x+20)

    =(x-1)(x²-10x+21)

    =(x-1)(x-3)(x-7)

    (2)原式

    =x³-2x²+4

    这个没法分解吧,我想不出怎么分解了

    (3)原式

    =x³-2x²-x²+4

    =x²(x-2)-(x²-4)

    =x²(x-2)-(x+2)(x-2)

    =(x-2)[x²-(x+2)]

    =(x-2)(x²-x-2)

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

    =(x+1)(x-2)²