求 $x^4-3x^3+9x^2-12x+27$ 除以 $x^2+5$ 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。

按最高次项依次相除。每一步都减去“本次商项乘除式”，最后余式次数必须低于二次。

Let $P(x)=x^4-3x^3+9x^2-12x+27$. The first quotient term is $x^2$:

The next quotient term is $-3x$:

The final quotient term is $4$:

Thus

The quotient is $\boxed{x^2-3x+4}$ and the remainder is $\boxed{3x+7}$.