待定系数法分解因式！急啊！！！

来源：百度知道 编辑：UC知道 时间：2024/05/12 12:32:02
4X^4+8X^3-X^2-8^X-3=？

前面三项没办法十字啊！急 ````哪位大虾指点个````

4X^4+8X^3-X^2-8^X-3

=4(x^4+2x^3+x^2)-(5x^2+8x+3)

=4x^2(x+1)^2-(5x+3)(x+1)

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

=(x+1)(4x^3+4x^2-5x-3)

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

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

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

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

(4X^4-X^2-3)用十字,(8X^3-8X)提公因式8X.

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