如何解x⁴-9x³-18x²-194x+192≤0?

1个回答

  • (x+4)(x+1)(x-8)(x-6)

    =(x²+5x+4)(x²-14x+48)

    =x²(x²-14x+48)+5x(x²-14x+48)+4(x²-14x+48)

    =x⁴-14x³+48x²+5x³-70x²+240x+4x²-56x+192

    因式分解过程如下:

    x^4-9x^3-18x^2+184x+192

    =x^4-8x^3-x^3+8x^2-26x^2+208x-24x+192

    =x^3(x-8)-x^2(x-8)-26x(x-8)-24(x-8)

    =(x-8)(x^3-x^2-26x-24)

    又x^3-x^2-26x-24

    =x^3-6x^2+5x^2-30x+4x-24

    =x^2(x-6)+5x(x-6)+4(x-6)

    =(x-6)(x^2+5x+4)

    =(x-6)(x+4)(x+1)

    ∴x^4-9x^3-18x^2+184x+192=(x-8)(x-6)(x+4)(x+1)