当前位置:首页 > 八年级 > 数学试卷

【330000】14.4.2用公式法分解因式

时间:2025-02-07 09:16:44 作者: 字数:2164字

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

14.4.2 用公式法分解因式

随堂检测

1、下列多项式中能用平方差公式分解因式的是( )

A. <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> B. <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> C. <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> D. <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

2、下列因式分解错误的是( )

A <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> B <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

C <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> D <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

3、把多项式 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 分解因式,结果正确的是( )

A <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> B <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> C <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> D <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

4、分解因式: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

5、分解因式 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

典例分析

例题2009年杭州市)在实数范围内因式分解 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> = _____________

分析:把一个多项式化为几个整式相乘的形式,叫做把这个多项式因式分解。所以 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ,可如果在实数范围内因式分解,就能够把2看成 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ,把 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 改写成 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ,从而继续因式分解了

解: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

课下作业

拓展提高

1、分解因式: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>


2、分解因式: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ____________


3、、因式分解: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>



4、利用因式分解计算: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>




5、求证:无论xy为何值, <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 的值恒为正





6、先化简再计算: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ,其中 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> =3 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> =2




7、在三个整式 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 中,请你任意选出两个进行加(或减)运算,使所得整式可以因式分解,并进行因式分解






体验中考

1、(山东枣庄)若m+n=3,则 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 的值为( )

A.12 B. <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> C.3 D.0

2(宁夏)分解因式: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>       

3、(黑龙江哈尔滨)把多项式x34x分解因式的结果为






















参考答案

随堂检测

1D

2D

3C  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

4 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

5 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> = <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</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/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

2 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

3

解:原式=

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

4、解:

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

5

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

因为 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> ,所以 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> 的值恒为正

6、解:原式= <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

xy2xy

=-x2y

因为 x3y2

所以原式=-341

7、解: <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

体验中考

1A  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

2 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>  <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a> = <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>

3 <a href="/tags/70/" title="公式" class="c1" target="_blank">公式</a> <a href="/tags/1603/" title="因式" class="c1" target="_blank">因式</a>