∵x2+x-2=(x+2)(x-1), ∴2x4-3x3+ax2+7x+b能被(x+2)(x-1)整除, 设商是A. 则2x4-3x3+ax2+7x+b=A(x+2)(x-1), 则x=-2和x=1时,右边都等于0,所以左边也等于0. 当x=-2时,2x4-3x3+ax2+7x+b=32+24+4a-14+b=4a+b+42=0 ① 当x=1时,2x4-3x3+ax2+7x+b=2-3+a+7+b=a+b+6=0 ② ①-②,得 3a+36=0, ∴a=-12, ∴b=-6-a=6. ∴==-2. 故答案为-2. |