已知A=x3-2x2+4x+3,B=x2+2x-6,C=x3+2x-3,求A-2B+3C的值,其中x=-2.

问题描述:

已知A=x3-2x2+4x+3,B=x2+2x-6,C=x3+2x-3,求A-2B+3C的值,其中x=-2.

∵B=x2+2x-6,∴2B=2x2+4x-12;∵C=x3+2x-3,∴3C=3x3+6x-9;由题意,得:A-2B+3C=x3-2x2+4x+3-(2x2+4x-12)+(3x3+6x-9),=x3-2x2+4x+3-2x2-4x+12+3x3+6x-9,=4x3-4x2+6x+6,=4x2(x-1)+6x+6,∵x=-2.∴原式=4...