设别的因式是Y
则2X^4+AX^3+BX^2+10X+4=Y(X^2+2X+1)(X+2)
2X^4+AX^3+BX^2+10X+4=Y(X+1)^2(X+2)
X=-1,则X+1=0
所以右边=0
所以左边也等于0
X=-1,
2X^4+AX^3+BX^2+10X+4=2-A+B-10+4=-A+B-4=0
A-B=-4 (1)
同理
X=-2,X+2=0,所以右边=0
所以左边=0
X=-2,
2X^4+AX^3+BX^2+10X+4=32-8A+4B-20+4=-8A+4B+16=0
2A-B=4 (2)
(2)-(1)
A=8,B=12