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【329999】14.4.1提公因式法分解因式

时间:2025-02-07 09:16:38 作者: 字数:1881字

 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

14.4.1提公因式法分解因式

随堂检测

1、把一个多项式化为几个 的形式,叫做把这个多项式因式分解

2、下列从左边到右边的变形,是因式分解的是( )

A <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>B <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

C <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>D <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

3、因式分解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> =

4、因式分解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>




典例分析

例题:已知(19x31)(13x17)(13x17)(11x23)可因式分解成(axb)(8xc),其中abc均为整数,则abc=

A12 B32 C38 D72

分析:可把整式(19x31)(13x17)(13x17)(11x23)分解因式成为两个一次二项式相乘的形式(即(axb)(8xc)的形式),用“若因式相同,则积相等”的原理得到abc的值即可。

至于是否abc的值只有这一种可能,因为是选择题,不用去考虑。

答案:A

因为

 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

又因为(19x31)(13x17)(13x17)(11x23)可因式分解成(axb)(8xc)

所以 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

可得 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

课下作业

拓展提高

1因式分解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

2、因式分解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>      

3、因式分解① <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>






 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>







4、已知 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ,求 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 的值







5、用因式分解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>


体验中考

1、(湖南株洲)分解因式: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>


2、(湖南长沙)因式分解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>




















参考答案

随堂检测

1、整式相乘

2B

3 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

4 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> = <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

课下作业

拓展提高

1 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

2 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

3

  1. 解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

  2. 解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

  3. 解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

  4. 解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

4、解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ,把 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 代入 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

原式 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

5、解: <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

体验中考

1 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

2 <a href="/tags/939/" title="公因式" class="c1" target="_blank">公因式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>