求 $3x^4-2x^2$ 除以 $x+1$ 所得的商和余数。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

补上缺失项的零系数后做综合除法，除数 $x+1$ 对应使用 $-1$。

Dividing by $x+1$, use the synthetic value $-1$ and coefficients $3,0,-2,0,0$:

Thus

The quotient is $\boxed{3x^3-3x^2+x-1}$ and the remainder is $\boxed{1}$.

先用余式定理求常数余式，再对商设一般形式并比较系数。

Let $f(x)=3x^4-2x^2$. By the remainder theorem, the remainder is

Write

Comparing coefficients gives

Therefore $A=3$, $B=-3$, $C=1$, $D=-1$. The constant coefficient checks since $D+1=0$.

Hence the quotient is $\boxed{3x^3-3x^2+x-1}$ and the remainder is $\boxed{1}$.