Course Content
第四章:部分分式 Partial Fraction
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第六章:角的形成及单位 Angles and Measurements
0/1
第十三章: 方程组 Simultaneous Equations
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第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
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高中一 | 高级数学
About Lesson
(1)
Use synthetic division to determine the quotient Q(x) and the remainder R obtained when the first polynomial is divided by the second polynomial.

用综合除法计算当第一多项式除以第二多项式除后所得的商式Q(x) 和余数R。

(a) 2x^3 - x^2 + 2x - 3 , x + 1

(b) x^4 + 3x^3 - x + 5, x - 3 [bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]没有x^2项,记得补0。[/bg_collapse]
(c) 2 - 3x + 5x^2 - 2x^3, 2x + 1 [bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]用-\frac{1}{3} 做综合除法后商式还需除2,余数不用除2[/bg_collapse]
(d) 4x^3 - 2x^2 + x - 1, 3x - 2 [bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]用 \frac{2}{3} 综合除法后因式还需除3,余式不用除3[/bg_collapse]

答案Answer:
(a) 2x^2 - 3x + 5 , -8

(b) x^3 + 6x^2 + 18x + 53 , 164

(c) -x^2 + 3x - 3 , 5

(d) \frac{4}{3}x^2+\frac{2}{9}x+\frac{13}{27} , -\frac{1}{27}
(2)
Use synthetic division to write the following expressions in the form Q\left(x\right)+\frac{R}{x-k}.
用综合除法把下列各因式写成 Q\left(x\right)+\frac{R}{x-k} 的模式。[bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Close Hint” ]Q(x) 为商式,R 为余数,x - k 为题目的分母。[/bg_collapse]

(a) \frac{x^3+5x^2+1}{x+2}

(b) \frac{4x^3+x^2-2x-7}{4x+1} [bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Close Hint” ]Hint:用 – ¼ 做综合除法后商式还需除4,余数不用除2. [/bg_collapse]

(c) \frac{x^4-2x^2+1}{1-2x} [bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Close Hint” ]没有x^3x项,记得补0。用½ 做综合除法后商式还需除-2,余数不用除-2 [/bg_collapse]

答案Answer:
(a) x^2-7x+14-\frac{27}{x-k}

(b) x^2-\frac{1}{2}-\frac{13}{2(4x+1)}

(c) -\frac{1}{2}x^3-\frac{1}{4}x^2+\frac{7}{8}x+\frac{7}{16}+\frac{9}{16(1-2x)}

(3)
If 2x^3 - ax^2- 5x - 2 has factor x + 1, find
x + 12x^3 - ax^2- 5x - 2 的因式,求

(a) the values of a,
a 之值,
[bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Close Hint” ]用 –1做综合除法,所得余数= 0.[/bg_collapse]

(b) factorize the statement.
该式因式的分解。
[bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Close Hint” ]将(a)综合除法所得商式因式分解。[/bg_collapse]

答案Answer:
(a) 1

(b) (2x + 1) (x - 2) (x + 1)
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