(时间:60分钟 满分:100分)
.选择题(15题30分)
1.x3-16x分解式结果正确( )
A.x(x2-16) B.x(x-4)2 C.x(x+4)2 D.x(x+4)(x-4)
2.a4b-6a3b+9a2b分解式正确结果 ( )
A.a2b(a2-6a+9) B.a2b(a-3)(a+3) C.b(a2-3)2 D.a2b(a-3)2
3.次课堂练颖学做4道式分解题认颖做够完整题( )
A.x2-y2=(x-y)(x+y) B.x2-2xy+y2=(x-y)2
C.x2y-xy2=xy(x-y) D.x3-x=x(x2-1)
4.整数m项式(4m+5)2-9定( )
A.8整 B.m整 C.(m-1)整 D.(2m-1)整
5.代数式3x3-6x2y+3xy2分解式结果正确 ( )
A.x(3x+y)(x-3y) B.3x(x2-2xy+y2)
C.x(3x-y)2 D.3x(x-y)2
6.列式中分解式结果2a(x-3)2 ( )
A.2ax2-6x+9 B.2ax2-18a C.2ax2+12ax+18a D.2ax2-12ax+18a
7.16-x4分解式结果 ( )
A.(2-x)4 B.(4+x2)(4-x2) C.(4+x2)(2+x)(2-x) D.(2+x)3(2-x)
8.代数式mx2-6mx+9m分解式列结果正确 ( )
A.m(x+3)2 B.m(x+3)(x-3) C.m(x-4)2 D.m(x-3)2
9.列代数式:①10am-15a②4xm2-9x③4am2-12am+9a④-4m2-9.中含式2m-3 ( )
A.1 B.2 C.3 D.4
10.(2x)n-81=(4x2+9)(2x+3)(2x-3)n值 ( )
A.2 B.4 C.6 D.8
11.列式中分解式正确 ( )
A.x2y2-2x2y+x2=x2(y2-2y) B.4(x2+1)-y2=(4x2+4+y)(4x2+4-y)
C.x4-8x2+16=(x2-4)2 D.-xn+1+xn1=-xn1(x+1)(x-1)
12 分解式结果(a+2)(b-3) ( )
A.-6+2b-3a+ab B.-6-2b+3a+ab C.ab-3b+2a-6 D.ab-2a+3b-6
13 a2+ab-ac-bc分解式结果( )
A.(a-b)(a-c) B.(a-b)(a+c)C.(a+b)(a-c) D.(a+b)(a+c)
14.a+b=6ab=7a2b+ab2值 ( )
A.13 B.1 C.42 D.54
15.项式4x3y-m分解成4xy(x2-y2+ab)m值 ( )
A.-4xy3+4abxy B.-4xy3-4abxy C.4xy3+4abxy D.4xy3-4abxy
二. 填空题(10题20分)
16式分解:x2y-9y=_______.
17xy=5a+b=4a-b=3a2xy-b2xy值_______.
18已知xy互相反数(x+2)2-(y+2)2=4x-y=__________.
19 已知a<0b<0较:-a3b3+2a2b2-ab_______0.
20.m= 时项式式.
21.项式x2+mx+5式分解(x+5)(x+n)m n .
22分解式:x2y-y=__________.
23分解式:a2(a-b)-4(a-b)=________.
24.分解式:2a2-4a+2=________
25.已知x2-x-1=0-x3+2x2+2020值________.
三 解答题(6题50分)
26(18分)列式分解式:
(1)3ax2-3ay4 (2)3ax2+6axy+3ay2 (3)x4-81
(4) x4-2x2+1 (5)m3-4m (6)2a2-4a+2
(7) x(x+y)(x-y)-x(x+y)2 (8) (a+1)(a-1)-8 (9)a3+ab2-2a2b
27 (6分)分解式: 正整数
28 (12分)先分解式计算求值.
(1)9x2+12xy+4y2中x= y=-
(2)()2-()2中a=-b=2
29 (6分)出三项式:x2+2x-1x2+4x+1x2-2x请选择喜欢两项式进行加法运算结果式分解.
30 (8分)探究性学 明学项式x2-xy+4x-4y分解式程:
x2-xy+4x-4y
=(x2-xy)+(4x-4y)(分成两组)
=x(x-y)+4(x-y)(直接提公式)
=(x-y)(x+4).
请明学解法启发列式分解式:
(1)m2-mn+mx-nx (2)x2-2xy+y2-9
教师样卷
.选择题(15题30分)
1.x3-16x分解式结果正确( D )
A.x(x2-16) B.x(x-4)2 C.x(x+4)2 D.x(x+4)(x-4)
[解析] x3-16x=x(x2-16)=x(x+4)(x-4).选D
2.a4b-6a3b+9a2b分解式正确结果 ( D )
A.a2b(a2-6a+9) B.a2b(a-3)(a+3) C.b(a2-3)2 D.a2b(a-3)2
[解析] 先提取公式a2b根完全方公式进行二次分解求答案.
a4b-6a3b+9a2b=a2b(a2-6a+9)=a2b(a-3)2选D
3.次课堂练颖学做4道式分解题认颖做够完整题( D )
A.x2-y2=(x-y)(x+y) B.x2-2xy+y2=(x-y)2
C.x2y-xy2=xy(x-y) D.x3-x=x(x2-1)
4.整数m项式(4m+5)2-9定( A )
A.8整 B.m整 C.(m-1)整 D.(2m-1)整
[解析] (4m+5)2-9=(4m+8)(4m+2)=8(m+2)(2m+1)m整数
(m+2)(2m+1)着m变化变化数该项式肯定8整.选A
5.代数式3x3-6x2y+3xy2分解式结果正确 ( D )
A.x(3x+y)(x-3y) B.3x(x2-2xy+y2)
C.x(3x-y)2 D.3x(x-y)2
6.列式中分解式结果2a(x-3)2 ( D )
A.2ax2-6x+9 B.2ax2-18a C.2ax2+12ax+18a D.2ax2-12ax+18a
7.16-x4分解式结果 ( C )
A.(2-x)4 B.(4+x2)(4-x2) C.(4+x2)(2+x)(2-x) D.(2+x)3(2-x)
8.代数式mx2-6mx+9m分解式列结果正确 ( D )
A.m(x+3)2 B.m(x+3)(x-3) C.m(x-4)2 D.m(x-3)2
9.列代数式:①10am-15a②4xm2-9x③4am2-12am+9a④-4m2-9.中含式2m-3 ( C )
A.1 B.2 C.3 D.4
10.(2x)n-81=(4x2+9)(2x+3)(2x-3)n值 ( B )
A.2 B.4 C.6 D.8
11.列式中分解式正确 ( D )
A.x2y2-2x2y+x2=x2(y2-2y) B.4(x2+1)-y2=(4x2+4+y)(4x2+4-y)
C.x4-8x2+16=(x2-4)2 D.-xn+1+xn1=-xn1(x+1)(x-1)
12 分解式结果(a+2)(b-3) ( A )
A.-6+2b-3a+ab B.-6-2b+3a+ab C.ab-3b+2a-6 D.ab-2a+3b-6
13 a2+ab-ac-bc分解式结果( C )
A.(a-b)(a-c) B.(a-b)(a+c)C.(a+b)(a-c) D.(a+b)(a+c)
14.a+b=6ab=7a2b+ab2值 ( C )
A.13 B.1 C.42 D.54
15.项式4x3y-m分解成4xy(x2-y2+ab)m值 ( D )
A.-4xy3+4abxy B.-4xy3-4abxy C.4xy3+4abxy D.4xy3-4abxy
二.填空题(10题20分)
16式分解:x2y-9y=_______.
[答案]y(x+3)(x-3)
17xy=5a+b=4a-b=3a2xy-b2xy值_______.
[答案]60
18已知xy互相反数(x+2)2-(y+2)2=4x-y=__________.
[答案]1
20 已知a<0b<0较:-a3b3+2a2b2-ab_______0.
[答案]≤
20.m= 时项式式.
[答案].1 解答:根系数特征判断x2-mx-6(x+2)(x-3)-m-1m1
21.项式x2+mx+5式分解(x+5)(x+n)m n .
[答案].61 解答:化简(x+5)(x+n)x2+(5+n)x+5n项式x2+mx+5应系数相等m6n1
22分解式:x2y-y=__________.
[答案] y(x+1)(x-1) [解析] x2y-y=y(x2-1)=y(x+1)(x-1).
23分解式:a2(a-b)-4(a-b)=________.
[答案] (a-b)(a-2)(a+2) [解析] a2(a-b)-4(a-b)=(a-b)(a2-4)=(a-b)(a-2)(a+2).
24.分解式:2a2-4a+2=________
[答案] 2(a-1)2 [解析] 原式=2(a2-2a+1)=2(a-1)2
25.已知x2-x-1=0-x3+2x2+2020值________.
[答案] 2021[解析] x2-x-1=0x2-x=1原式=-x(x2-x)+x2+2020=-x+x2+2020=2021
三.解答题(6题50分)
26(18分)列式分解式:
(1)3ax2-3ay4 (2)3ax2+6axy+3ay2 (3)x4-81
(5) x4-2x2+1 (5)m3-4m (6)2a2-4a+2
(7)x(x+y)(x-y)-x(x+y)2 (8) (a+1)(a-1)-8 (9)a3+ab2-2a2b
解: (1)3ax2-3ay4=3a(x2-y4)=3a(x+y2)(x-y2).
(2)3ax2+6axy+3ay2=3a(x2+2xy+y2)=3a(x+y)2
(3)x4-81=(x2+9)(x2-9)=(x2+9)(x+3)(x-3).
(4)x4-2x2+1=(x2-1)2=(x+1)2(x-1)2
(5)原式=m(m2-4)=m(m+2)(m-2)
(6)原式=2(a2-2a+1)=2(a-1)2
(7)原式=x(x+y)[x-y-(x+y)]=x(x+y)(x-y-x-y)=-2xy(x+y)
(8)原式=a2-1-8=a2-9=(a+3)(a-3)
(9)原式=a(a2+b2-2ab)=a(a-b)2
27 (6分)分解式: 正整数
答案 解析正整数时偶数奇数
28 (12分)先分解式计算求值.
(1)9x2+12xy+4y2中x= y=-
(2)()2-()2中a=-b=2
解:(1)原式=(3x+2y)2 x=y=-时原式=[3×+2×(-)]2=(4-1)2=9
(2)原式=(+)(-)=aba=-b=2时原式=(-)×2=-
29 (6分)出三项式:x2+2x-1x2+4x+1x2-2x请选择喜欢两项式进行加法运算结果式分解.
答案唯举例:选择x2+2x-1x2+4x+1
x2+2x-1+(x2+4x+1)=x2+2x-1+x2+4x+1=x2+6x=x(x+6)
30 (8分)探究性学 明学项式x2-xy+4x-4y分解式程:
x2-xy+4x-4y
=(x2-xy)+(4x-4y)(分成两组)
=x(x-y)+4(x-y)(直接提公式)
=(x-y)(x+4).
请明学解法启发列式分解式:
(1)m2-mn+mx-nx (2)x2-2xy+y2-9
解:(1)m2-mn+mx-nx=m(m-n)+x(m-n)=(m-n)(m+x).
(2)x2-2xy+y2-9=(x-y)2-32=(x-y+3)(x-y-3).
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