因式分解:4x^4-x^2+2x-1

1个回答

  • 4x^4-x^2+2x-1

    =x^2(4x^2-1)+(2x-1)

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

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

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

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

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

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

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

    =(2x-1){(x+1)[2x(x-1)+x+1}

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

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

    如果楼主是在实数范围内分解,到此步可以停止;

    若是复数可继续分解.