Tag Archive: 除法原理

108-學測-數學-12

設${{f}_{1}}(x),{{f}_{2}}(x)$為實係數三次多項式,$g(x)$為實係數二次多項式。已知${{f}_{1}}(x),{{f}_{2}}(x)$除以$g(x)$的餘式分別為${{r}_{1}}(x),{{r}_{2}}(x)$。試選出正確的選項。
(1) $-{{f}_{1}}(x)$除以$g(x)$的餘式為$-{{r}_{1}}(x)$
(2) ${{f}_{1}}(x)+{{f}_{2}}(x)$除以$g(x)$的餘式為${{r}_{1}}(x)+{{r}_{2}}(x)$
(3) ${{f}_{1}}(x){{f}_{2}}(x)$除以$g(x)$的餘式為${{r}_{1}}(x){{r}_{2}}(x)$
(4) ${{f}_{1}}(x)$除以$-3g(x)$的餘式為$\frac{-1}{3}{{r}_{1}}(x)$
(5) ${{f}_{1}}(x){{r}_{2}}(x)-{{f}_{2}}(x){{r}_{1}}(x)$可被$g(x)$整除