x^4+2x^3-9x^2-2x+8

来源：百度知道 编辑：UC知道 时间：2024/06/05 10:38:10
x^4+2x^3-9x^2-2x+8 过程谢谢

原式=(X^4-X^2)+(2X^3-2X)-(8X^2-8)
=X^2(X^2-1)+2X(X^2-1)-8(X^2-1)
=(X^2+2X-8)(X^2-1)
=(X^2+2X+1-9)(X^2-1)
=[(X+1)^2-9](X^2-1)
=(X+1+3)(X+1-3)(X+1)(X-1)
=(X+4)(X-2)(X+1)(X-1)

x^4+2x^3-9x^2-2x+8
=(x^4-x^3)+(3x^3-3x^2)-(6x^2-6x)-(8x-8)
=x^3(x-1)+3x^2(x-1)-6x(x-1)-8(x-1)
=(x-1)(x^3+3x^2-6x-8)
=(x-1)[(x^3-8)+(3x^2-6x)]
=(x-1)[(x-2)(x^2+2x+4)+3x(x-2)]
=(x-1)(x-2)(x^2+2x+4+3x)
=(x-1)(x-2)(x^2+5x+4)
=(x-1)(x-2)(x+1)(x+4)