求 $2x^4-27$ 除以 $x^2+x+3$ 所得的商和余式。

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。

依次用最高次项相除，并在每一步减去商项乘除式，直到余式次数低于二次。

The first quotient term is $2x^2$:

The next term is $-2x$:

The final term is $-4$:

Therefore

The quotient is $\boxed{2x^2-2x-4}$ and the remainder is $\boxed{10x-15}$.

把被除式写为除式乘二次商再加一次余式，比较各次幂系数，依次求出五个常数。

Write

Comparing coefficients gives

Thus $B=-2$, $C=-4$, $D=10$ and $E=-15$. The quotient is $\boxed{2x^2-2x-4}$ and the remainder is $\boxed{10x-15}$.