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) ,
(b) ,
[bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]没有
项,记得补0。[/bg_collapse]
(c) ,
[bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]用
做综合除法后商式还需除2,余数不用除2[/bg_collapse]
(d) ,
[bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]用
综合除法后因式还需除3,余式不用除3[/bg_collapse]
答案Answer:
![Rendered by QuickLaTeX.com 2x^2 - 3x + 5](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3d89e9147882e1d1a7d4d22f11ea0f4d_l3.png)
![Rendered by QuickLaTeX.com -8](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-364da3256b70be64b2e715e5dd22205b_l3.png)
(b)
![Rendered by QuickLaTeX.com x^3 + 6x^2 + 18x + 53](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-540ead9528a91eb0458ba37bca8d4db3_l3.png)
![Rendered by QuickLaTeX.com 164](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-4bd7e29fed9cab0994d477a7bb4e5bee_l3.png)
(c)
![Rendered by QuickLaTeX.com -x^2 + 3x - 3](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-10064e84d73bcf1ccde3f906958b38df_l3.png)
![Rendered by QuickLaTeX.com 5](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-2fa2fd276df03051eaa5e59c5edf78a5_l3.png)
(d)
![Rendered by QuickLaTeX.com \frac{4}{3}x^2+\frac{2}{9}x+\frac{13}{27}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-9aac1ddb7844fcdfb44fa3add37afea5_l3.png)
![Rendered by QuickLaTeX.com -\frac{1}{27}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3879717e4d7d8f6267b066aa4debd13c_l3.png)
Use synthetic division to write the following expressions in the form
![Rendered by QuickLaTeX.com Q\left(x\right)+\frac{R}{x-k}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7da60e77b8eab500c81f49b0f5cb2cba_l3.png)
用综合除法把下列各因式写成
![Rendered by QuickLaTeX.com Q\left(x\right)+\frac{R}{x-k}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7da60e77b8eab500c81f49b0f5cb2cba_l3.png)
![Rendered by QuickLaTeX.com Q(x)](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-0382545558ade970534dd4da8371e4a8_l3.png)
![Rendered by QuickLaTeX.com R](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ef0fc2f7a5ea245dd34aa7051faa841c_l3.png)
![Rendered by QuickLaTeX.com x - k](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f569dd7bcba303db3e745b84823639d6_l3.png)
(a)
(b) [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) [bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Close Hint” ]没有
和
项,记得补0。用½ 做综合除法后商式还需除
,余数不用除
[/bg_collapse]
答案Answer:
![Rendered by QuickLaTeX.com x^2-7x+14-\frac{27}{x-k}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-4b717a7c13e83044bc7633cefb27c7b5_l3.png)
(b)
![Rendered by QuickLaTeX.com x^2-\frac{1}{2}-\frac{13}{2(4x+1)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-a6f466029f0f7662e228d245903b0bb8_l3.png)
(c)
![Rendered by QuickLaTeX.com -\frac{1}{2}x^3-\frac{1}{4}x^2+\frac{7}{8}x+\frac{7}{16}+\frac{9}{16(1-2x)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1fdbee16877c6834f7759a0da0392e7e_l3.png)
(3)
If has factor
, find
若为
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:
![Rendered by QuickLaTeX.com 1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7297ed5d8a0649a927d31ac326d7d575_l3.png)
(b)
![Rendered by QuickLaTeX.com (2x + 1) (x - 2) (x + 1)](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-bd2a1ec55e4f91bec09b7720241e5d47_l3.png)