初二数学整式的除法专题训练文档格式.docx
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(m2+m-1)的余式是2m+4,则b=______.
19.已知(3x3+nx+20)÷
(x2+2x-3)所得余式为3x+2,则n=______.
20.如果4x3+9x2+mx+n能被x2+2x-3整除,则m=______,n=______.
21.x3+4x2+5x+2用整式______除,则商式和余式都是x+1.
22.已知(3x3+nx+m)÷
(x2+2x-3)所得余式为3x+2,则m=______,n=______.
23.已知x2-3x-2=0,则-x3+11x+6=______.
(二)选择
24.21a8÷
7a2=
[
]
A.7a4;
B.3a6;
C.3a10;
D.3a16.
25.x9y3÷
x6y2=
A.x3y;
B.x3y3;
C.x3y2;
D.x3.
26.28a4b2÷
7a3b=
A.4ab2;
B.4a4b;
C.4a4b2;
D.4ab.
A.8xyz;
B.-8xyz;
C.2xyz;
D.8xy2z2.
28.25a3b2÷
5(ab)2=
A.a;
B.5a;
C.5a2b;
D.5a2.
29.正确地进行整式运算可得
A.2x+3y=5xy;
B.4x3y-5xy3=-xy;
C.3x3·
2x2=6x6;
D.4x4y3÷
(-2xy3)=-2x3.
30.下列计算正确的是
A.aman=a2m;
B.(a3)2=a5;
C.a3m-5÷
a5-m=a4m-10;
D.x3x4x5=x60.
31.下列计算错误的是
A.(x4)4=x16;
B.a5a6÷
(a5)2÷
a=a2;
C.(-a)(-a2)+a3+2a2(-a)=0;
D.(x5)2+x2x3+(-x2)5=x5.
32.(x4y+6x3y2-x2y3)÷
3x2y=
A.x2+2xy-y2;
34.下列整式除法正确的是
A.(3x2y3+6x2y2)÷
3xy2=xy+2xy;
B.(5a2b4-25a3)÷
(-5b4)=-a2+5a3b4;
C.(2x2-5x-3)÷
(x-3)=2x+1;
D.(a+b)4(a-b)÷
2(a+b)(a2-b2)=2(a+b)2×
(a-b).
35.(2x3-5x2+3x-2)÷
(-x+1+2x2)=
A.x+1;
B.x-1;
C.x+2;
D.x-2.
36.(x2+2xy-8y2+2x+14y-3)÷
(x-2y+3)=
A.x-4y-1;
B.x+4y+1;
C.x+y;
D.x+4y-1.
37.(x3+2x2+x+1)÷
(x2+x-1)的余式是
38.(1+x+2x2+x3)÷
B.x+2;
C.x-1;
39.除式=6x2+3x-5,商式=4x-5,余式=-8,则被除式为
A.(6x2+3x-5)(4x-5)+8;
B.(6x2+3x-5)÷
(4x-5)-8;
C.(6x2+3x-5)+(4x-5)×
(-8);
D.(6x2+3x-5)(4x-5)-8.
40.(x3-2x2+ax+2)÷
(x2-4x+1)=x+2,则
A.a=-7;
B.a=7;
C.a=7x;
D.a=-7x.
41.(x3-3x2-9x+23)=(x2-x-11)·
N+1,则N=
A.x-2;
C.-x-2;
D.-x+2.
42.若x3-3x2+ax+b能被x-2整除,则
A.a=9,b=22;
B.a=9,b=-22;
C.a=-9,b=22;
D.a=-9,b=-22.
43.9x4-6x2y2+y4=(3x2-y2)·
M,则M=
A.3x2+y2;
B.(3x)2-y2;
C.(3x)2+y2;
D.3x2-y2.
44.如果4x3+9x2+mx+n能被x2+2x-3整除,则
A.m=10,n=3;
B.m=-10,n=3;
C.m=-10,n=-3;
D.m=10,n=-3.
45.(3x-4x2+x4-4)=M·
(x2+2x-1)+(-x-3),则M为
A.x2+2x+1;
B.x2-2x+1;
C.-x2+2x+1;
D.x2+2x-1.
46.多项式x2+x+m能被x+5整除,则此多项式也能被下述多项式整除的是
]
A.x-6;
B.x+6;
C.x-4;
D.x+4.
47.3x4-2x3-32x2+66x+m能被x2+2x-7整除,则m为
A.35;
B.-32;
C.-35;
D.32.
(三)计算
48.-3(ab)2·
(3a)2·
(-ab)3÷
(12a3b2).
50.(2mn)2·
(m2+n2)-(m2n2)3÷
m3n4+3m2n4.
51.162m÷
82n÷
4m×
43(n-m+1).
整数).
53.(4xn-1yn+2)2÷
(-xn-2yn+1).
54.[2yx3+(-2y3-2y2-1)x2+(2y4+y2+y)x-y3]÷
(2xy-1)÷
(x-y).
55.(x2a+3b+4c)m÷
[(xa)2m·
(x3)bm·
(xm)4c].
56.四个连续奇数的第二个数是2n+1,已知前两个数的积比后两个数的积少64,求这四个奇数.
57.利用竖式除法计算(4+2x3-5x2)÷
(x-2).
58.用竖式除法计算(2a3+3a-3+9a2)÷
(4a+a2-3).
59.(6x4-3x3-7x-3)÷
(2x2-x-2).
60.长方形面积是x2-3xy+2y2,它的一边长是x-y,求它的周长.
61.(a5-2a4b-4a3b2+b5)÷
(a3+2ab2+b3).
62.x(13x2+3x3-1)÷
(x2+4x-3).
63.(2x4+7x3-12x2-27x)÷
(2x2+3x)÷
64.(x5+x4+5x2+5x+6)÷
(x2+x+1)÷
(x+2).
65.已知整式A=x3-1+x-x2,B=x2-3x+5,求A÷
B的商和余式.
66.求[4yx4-2x3+yx2-1]÷
(x-y)÷
(2xy-1)的商式和余式.
67.已知除式=3x2+2y,商式=9x4-6x2y+4y2,余式=x-8y3,求被除式.
68.已知除式=2x3-3x2+1,商式=x+2,余式=6x2-2,求被除式.
69.已知被除式=x4+y4,商式=x3+x2y+xy2+y3,余式=2y4,求除式.
70.已知被除式=18x4+82x2+56-71x-45x3,商式=6x2-7x+8,余式=16-4x,求除式.
71.一个多项式除以x2+3x-5,商式为x2+x+1,余式为2x-1,求这个多项式.
73.已知被除式=4x3+2x2-1,除式=2x-4,余式=39,求商式.
74.已知被除式=x5-4x3+2x2+1,除式=x+2,商式=x4-2x3+2x-4,求余式.
75.已知x-2能整除x2+kx-14,求k的值.
76.已知3x-1能整除6x2+13x+b,求b的值.
77.求多项式[2x4-5x3-26x2-x+28]÷
(x-1)÷
(2x+3)÷
(x+2)的商式和余式.
78.已知多项式3x3-13x2+18x+m能被(x-1)(x-2)整除,其商为3x+n,求m,n的值.
79.已知多项式x3+3x2+ax+b能被x+2整除,且商式被(x-3)除时余3,求a,b的值.
80.若多项式(a+b)x2+2bx-3a以x+1和x+2除之分别余1和-22,试求a,b的值.
81.已知x3+(a+b)x2+(-2a+b)x+3a-b能被(x-1)2整除,求a,b的值.
82.已知多项式x3+ax2-(a+2)x+3a-6能被x2+2x+3整除,且商式为Ax+B,求A,B的值.
83.如果多项式x2-2(m+1)x+m能被x+1整除,求m的值.
84.已知被除式=-2y4-y3+5y2+5y+5,商式=y2-2,余式=3y+7,求除式.
85.已知x2-3x-2=0,求-x3+11x+6的值.
86.已知被除式=x4-2x3y-x2y+y2,除式=x2-2y,余式=-4xy2+3y2,求商式.
87.已知多项式F被x2-2x-3除时余式为x+4,试求F被x+1除时的余式.
88.已知被除式=x4-3x2+ax-1,除式=bx+1,商式=x3-x2-2x+4,余式=-5,求a,b的值.
整式的除法专题训练答案
1.x2
2.18xyz2
3.-2a3
4.25x3y3
5.y2n+4
6.5m3y5z5
7.-2a+3
8.m-n
9.-1
10.-2x2+3xy-y2
11.-1
12.a+2
13.3x2-2x+1;
3x3+7x2-6x-2
14.x-y
15.-2
17.2x2+4x-3
18.4
19.-18
20.-10,-3
21.x2+3x+1
22.20,-18
23.0
24.B25.A26.D27.A
28.B29.D30.C31.B
32.C33.B34.C35.D
36.D37.C38.B39.D
40.A41.A42.C43.D
44.C45.B46.C47.C
49.8.
50.4m4n2+7m2n4-m3n2.
51.64.
52.4+23m+2n-1.
53.-16xnyn+3.
54.x-y2.
55.1.
56.5,7,9,11.
提示:
依题意得
(2n+3)(2n+5)-(2n-1)(2n+1)=64.
解得n=3.所以四个奇数分别为
2n-1=5,2n+1=7,2n+3=9,2n+5=11.
57.2x2-x-2.
58.商式=2a+1,余式=5a.
59.商式=3x2+3,余式=-4x+3.
60.4x-6y.
61.商式=a2-2ab-6b2,余式=3a2b3+14ab4+7b5.
62.商式=3x2+x+5,余式=-18x+15.
63.商式=x+4,余式=-2x2-3x.
64.x2-2x+3.
65.商式=x+2,余式=2x-11.
67.27x6+x.
68.2x4+x3+x.
69.x-y.
70.3x2-4x+5.
71.x4+4x3-x2-6.
73.2x2+5x+10.
74.9.
75.k=5.
76.b=-5.
77.商式=x-5,余式=-2.
78.m=-8,n=-4.
提示3x3-13x2+18x+m=(x-1)(x-2)(3x+n)=3x3+(n-9)x2+(6-3n)x+2n.
79.a=-7,b=-18.
80.a=-22,b=43.
81.a=0,b=-1.
83.-1.
84.-2y2-y+1.
85.0.
原式=(-x3+3x2+2x)-(3x2-9x-6)=-x(x2-3x-2)-3(x2-3x-2).再把已知条件x2-3x-2=0代入,得值等于0.
86.x2-2xy+y.
87.余式=3.
设F被x2-2x-3除得的商式为q,又余式为x+4,所以F=q(x2-2x-3)+x+4=q(x+1)(x-3)+(x+1)+3=(x+1)[q(x-3)+1]+3,即余式=3.
88.a=2,b=1.
x4-3x2+ax-1=(bx+1)(x3-x2-2x+4)+(-5).
右边展开后与左边对比同类项系数可得结果.
89.
(1)当m<2时,有正数解.
(2)当m=8时,无解.
90.
(1)a是大于-4的整数.
>0时,y>0,这就有a>-4.