解题方法
1 . 秦九韶是我国南宋时期的数学家,他在所著的《数书九章》中提出的多项式求值的秦九韶算法,具有世界意义的重要贡献.如图是实现该算法的程序框图.执行该程序框图,若输入的
,
,依次输入的
为2,3,4,则输出的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c7e7449010436e00dce3b6924a4258.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c7e7449010436e00dce3b6924a4258.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/095094b9-bd95-43c8-a6d3-8a2dbd525004.png?resizew=113)
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名校
解题方法
2 . 中国古代有计算多项式值的秦九韶算法,如图是实现该算法的程序框图.执行该程序框图,若输入
,
,依次输入
的值为1,2,3,则输出的
( )
![](https://img.xkw.com/dksih/QBM/2021/4/22/2705325970808832/2710164007010304/STEM/3782e051-7975-4add-9cef-69ed1d49a34f.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c7e7449010436e00dce3b6924a4258.png)
![](https://img.xkw.com/dksih/QBM/2021/4/22/2705325970808832/2710164007010304/STEM/3782e051-7975-4add-9cef-69ed1d49a34f.png?resizew=164)
A.10 | B.11 | C.16 | D.17 |
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3 . 下列说法正确的是( )
①
;
②用辗转相除法求得459和357的最大公约数是61;
③能使
的值为3的赋值语句是
;
④用秦九韶算法求多项式
在
的值时,
的值是5;
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddb019e576f8db9f0a05dd9d0256e36.png)
②用辗转相除法求得459和357的最大公约数是61;
③能使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c2d44bf93ef5661ec97254b9d1d513.png)
④用秦九韶算法求多项式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b95581f35ae79874008f5dd98885166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f6ccbb4c090d2e66cda9e5acf44458.png)
A.①② | B.②③ | C.①④ | D.②④ |
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4 . 用秦九韶算法计算函数
,当
时的值,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da91748e6e8547740d57566df289921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5708167a5cc48a1e08b688df3b4c289.png)
A.-2 | B.-1 | C.0 | D.1 |
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解题方法
5 . 《数书九章》是我国宋代数学家秦九韶的著作,其中给出了求多项式值的秦九韶算法,如图所示的程序框图给出了一个利用秦九韶算法求某多项式值的实例,若输入的
,则输出的
值是( )
![](https://img.xkw.com/dksih/QBM/2020/7/7/2500980266041344/2501469247258624/STEM/d2cab7f2-c6c1-4e1b-a2b6-21890345d0ac.png?resizew=282)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/2020/7/7/2500980266041344/2501469247258624/STEM/d2cab7f2-c6c1-4e1b-a2b6-21890345d0ac.png?resizew=282)
A.22 | B.46 | C.94 | D.190 |
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6 . 秦九韶是我国南宋时期的数学家,普州(现四川省安岳县)人,他在所著的《数书九章》中提出的多项式求值的秦九韶算法,至今仍是比较先进的算法.已知一个5次多项式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f2d63ae1459566026715ba472d7c26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e9a8e2708ca3c74a2d280abe2d29b5.png)
,用秦九韶算法求这个多项式当
时的值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f2d63ae1459566026715ba472d7c26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e9a8e2708ca3c74a2d280abe2d29b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581f8c33e1438f9db75243f109bdc49f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
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7 . 用秦九韶算法计算多项式
,当
时的求值的过程中,
的值为________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d331792a7f516467382283e66ff0f518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ff06692c025b869a7bcdcff15dca9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814f55724f7ee57bd395eb3b95393c68.png)
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8 . 秦九韶是我国古代的数学家,他的《数书九章》概括了宋元时期中国传统数学的主要成就. 秦九韶算法是一种将一元
次多项式的求值问题转化为
个一次式的算法,其大大简化了计算过程,即使在现代,利用计算机解决多项式的求值问题时,秦九韶算法依然是最优的算法,在西方被称作霍纳算法.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251306650fdd855a04dcd1697e5d73ef.png)
改写成以下形式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251306650fdd855a04dcd1697e5d73ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7644b2adbf6932b5c4b56c01295a8a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecedcaaa90738e92bc254db62d75857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed8181dab2251aad31eef4d43413cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa870171979b115b0c3440705bc8face.png)
若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3398169945f7a03c882318c77d6115.png)
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6306ddd63cd3b16a74f48f4bb20f81.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251306650fdd855a04dcd1697e5d73ef.png)
改写成以下形式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/251306650fdd855a04dcd1697e5d73ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7644b2adbf6932b5c4b56c01295a8a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecedcaaa90738e92bc254db62d75857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed8181dab2251aad31eef4d43413cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa870171979b115b0c3440705bc8face.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3398169945f7a03c882318c77d6115.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6306ddd63cd3b16a74f48f4bb20f81.png)
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9 . 秦九韶是我国南宋时期的数学家,他在所著的《数书九章》中提出的多项式求值的秦九韶算法,至今仍是比较先进的算法.如图所示的程序框图给出了利用秦九韶算法求某多项式值的一个实例,若输入
的值分别为
,
,则输出
的值为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/c12f9ca8-23a4-4e00-9b8b-d508154d168d.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3853adfe362bcb9fda0d61f0aa7c7026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc13a607ac0c7f76d252d7cb1bb040fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/c12f9ca8-23a4-4e00-9b8b-d508154d168d.png?resizew=164)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 用秦九韶算法求多项式
当
时的值时,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0982e80a665963a5dbd5462e603111e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5708167a5cc48a1e08b688df3b4c289.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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