标题

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中考复习:2018年全国各省市中考真题汇编—因式分解

一、知识点分析

二、难易度分析

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2018年中考真题汇编专题复习—因式分解

一.选择题(共5小题)

1.(2018•贺州)下列各式分解因式正确的是\((\)  \()\)

A.\({x^2} + 6xy + 9{y^2} = {(x + 3y)^2}\)   

B.\(2{x^2} – 4xy + 9{y^2} = {(2x – 3y)^2}\) 

C.\(2{x^2} – 8{y^2} = 2(x + 4y)(x – 4y)\)       

D.\(x(x – y) + y(y – x) = (x – y)(x + y)\)

2.(2018•邵阳)将多项式\(x – {x^3}\)因式分解正确的是\((\)  \()\)

A.\(x({x^2} – 1)\)     

B.\(x(1 – {x^2})\)     

C.\(x(x + 1)(x – 1)\) 

D.\(x(1 + x)(1 – x)\)

3.(2018•济宁)多项式\(4a – {a^3}\)分解因式的结果是\((\)  \()\)

A.\(a(4 – {a^2})\)       

B.\(a(2 – a)(2 + a)\)   

C.\(a(a – 2)(a + 2)\)   

D.\(a{(2 – a)^2}\)

4.(2018•安徽)下列分解因式正确的是\((\)  \()\)

A.\( – {x^2} + 4x =  – x(x + 4)\)                       

B.\({x^2} + xy + x = x(x + y)\)                           

C.\(x(x – y) + y(y – x) = {(x – y)^2}\)               

D.\({x^2} – 4x + 4 = (x + 2)(x – 2)\)

5.(2018•百色)因式分解\(x – 4{x^3}\)的最后结果是\((\)  \()\)

A.\(x{(1 – 2x)^2}\)    

B.\(x(2x – 1)(2x + 1)\)   

C.\(x(1 – 2x)(2x + 1)\)                                                

D.\(x(1 – 4{x^2})\)

二.填空题(共43小题)

6.(2018•青海)分解因式:\({x^3}y – 4xy = \)  ;不等式组\(\left\{\begin{array}{l}{x-2<0}\\ {2x+6\geq0}\end{array}\right.\)的解集是  

7.(2018•绥化)因式分解:\(3a{x^2} – 12a{y^2} = \)  

8.(2018•常州)分解因式:\(3{x^2} – 6x + 3 = \)  

9.(2018•赤峰)分解因式:\(2{a^2} – 8{b^2} = \)  

10.(2019•梁平区)在实数范围内分解因式:\({x^2} – 2x – 1 = \)   

11.(2018•兰州)因式分解:\({x^2}y – {y^3} = \)  

12.(2018•巴彦淖尔)分解因式:\(8{a^2} – 8{a^3} – 2a = \)  

13.(2018•遂宁)分解因式\(3{a^2} – 3{b^2} = \)  

14.(2018•苏州)若\(a + b = 4\),\(a – b = 1\),则\({(a + 1)^2} – {(b – 1)^2}\)的值为  

15.(2018•哈尔滨)把多项式\({x^3} – 25x\)分解因式的结果是  

16.(2018•吉林)若\(a + b = 4\),\(ab = 1\),则\({a^2}b + a{b^2} = \)  

17.(2018•怀化)因式分解:\(ab + ac = \)  

18.(2018•张家界)因式分解:\({a^2} + 2a + 1 = \)  

19.(2018•恩施州)因式分解:\(8{a^3} – 2a{b^2} = \)  

20.(2018•株洲)因式分解:\({a^2}(a – b) – 4(a – b) = \)  

21.(2018•河北)若\(a\),\(b\)互为相反数,则\({a^2} – {b^2} = \)  

22.(2018•湘潭)因式分解:\({a^2} – 2ab + {b^2} = \)  

23.(2018•温州)分解因式:\({a^2} – 5a = \)  

24.(2018•潍坊)因式分解:\((x + 2)x – x – 2 = \)  

25.(2018•扬州)因式分解:\(18 – 2{x^2} = \)  

26.(2018•盘锦)因式分解:\({x^3} – x = \)  

27.(2018•巴中)分解因式:\(2{a^3} – 8a = \)  

28.(2018•无锡)因式分解:\({x^3} – 4x = \)  

29.(2018•攀枝花)分解因式:\({x^3}y – 2{x^2}y + xy = \)  

30.(2018•辽阳)分解因式:\(4a{x^2} – a{y^2} = \)   

31.(2018•自贡)分解因式:\(a{x^2} + 2axy + a{y^2} = \)   

32.(2018•黄石)分解因式:\({x^3}y – x{y^3} = \)  

33.(2018•宜宾)分解因式:\(2{a^3}b – 4{a^2}{b^2} + 2a{b^3} = \)  

34.(2018•黄冈)因式分解:\({x^3} – 9x = \)  

35.(2018•沈阳)因式分解:\(3{x^3} – 12x = \)  

36.(2018•淄博)分解因式:\(2{x^3} – 6{x^2} + 4x = \)  

37.(2018•菏泽)若\(a + b = 2\),\(ab =  – 3\),则代数式\({a^3}b + 2{a^2}{b^2} + a{b^3}\)的值为  

38.(2018•绍兴)因式分解:\(4{x^2} – {y^2} = \)  

39.(2018•杭州)因式分解:\({(a – b)^2} – (b – a) = \)  

40.(2018•威海)分解因式:\( – \frac{1}{2}{a^2} + 2a – 2 = \)  

41.(2018•成都)已知\(x + y = 0.2\),\(x + 3y = 1\),则代数式\({x^2} + 4xy + 4{y^2}\)的值为  

42.(2018•绵阳)因式分解:\({x^2}y – 4{y^3} = \)  

43.(2018•益阳)因式分解:\({x^3}{y^2} – {x^3} = \)  

44.(2018•德阳)分解因式:\(2x{y^2} + 4xy + 2x = \)  

45.(2018•本溪)分解因式:\(2{a^2} – 8ab + 8{b^2} = \)   

46.(2018•抚顺)分解因式:\(x{y^2} – 4x = \)  

47.(2018•郴州)因式分解:\({a^3} – 2{a^2}b + a{b^2} = \)  

48.(2018•毕节市)因式分解:\({a^3} – a = \)   

三.解答题(共2小题)

49.(2018•大连)【观察】\(1 \times 49 = 49\),\(2 \times 48 = 96\),\(3 \times 47 = 141\),\( \ldots \),\(23 \times 27 = 621\),\(24 \times 26 = 624\),\(25 \times 25 = 625\),\(26 \times 24 = 624\),\(27 \times 23 = 621\),\( \ldots \),\(47 \times 3 = 141\),\(48 \times 2 = 96\),\(49 \times 1 = 49\).

【发现】根据你的阅读回答问题:

(1)上述内容中,两数相乘,积的最大值为  

(2)设参与上述运算的第一个因数为\(a\),第二个因数为\(b\),用等式表示\(a\)与\(b\)的数量关系是  

【类比】观察下列两数的积:\(1 \times 59\),\(2 \times 58\),\(3 \times 57\),\(4 \times 56\),\( \ldots \),\(m \times n\),\( \ldots \),\(56 \times 4\),\(57 \times 3\),\(58 \times 2\),\(59 \times 1\).

猜想\(mn\)的最大值为  ,并用你学过的知识加以证明.

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50.(2018•临安区)阅读下列题目的解题过程:

已知\(a\)、\(b\)、\(c\)为\(\Delta ABC\)的三边,且满足\({a^2}{c^2} – {b^2}{c^2} = {a^4} – {b^4}\),试判断\(\Delta ABC\)的形

状.

解:∵\( a^{2}c^{2}-b^{2}c^{2}=a^{4}-b^{4}\) (A)

∴\( {c^2}({a^2} – {b^2}) = ({a^2} + {b^2})({a^2} – {b^2})\) (B)

∴\( {c^2} = {a^2} + {b^2}\) (C)

∴\( \Delta ABC\)是直角三角形

问:(1)上述解题过程,从哪一步开始出现错误?请写出该步的代号:  

(2)错误的原因为:  

(3)本题正确的结论为:  

2019.3.19




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