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1、因式分解3a3b2c6a2b2c29ab2c33ab2 c(a2-2ac+3c2) 3.因式分解xy62x3y(x-3)(y-2) 4.因式分解x2(xy)y2(yx)(x+y)(x-y)2 5.因式分解2x2(a2b)xab(2x-a)(x+b) 6.因式分解a49a2b2a2(a+3b)(a-3b) 7.若已知x33x24含有x1的因式,试分解x33x24(x-1)(x+2)2 8.因式分解ab(x2y2)xy(a2b2)(ay+bx)(ax-by) 9.因式分解(xy)(abc)(xy)(bca)2y(a-b-c) 10.因式分解a2ab2b(a+b)(a-b-1) 11.因式分解(3a
2、b)24(3ab)(a3b)4(a3b)23a-b-2(a+3b)2=(a-7b)2 12.因式分解(a3)26(a3)(a+3)(a-3) 13.因式分解(x1)2(x2)(x1)(x2)2-(x+1)(x+2) abcab4aa(bc+b-4) (2)16x281(4x+9)(4x-9) (3)9x230x25(3x-5)2 (4)x27x30(x-10)(x+3) 35.因式分解x225(x+5)(x-5) 36.因式分解x220x100(x-10)2 37.因式分解x24x3(x+1)(x+3) 38.因式分解4x212x5(2x-1)(2x-5) 39.因式分解下列各式: (1)3a
3、x26ax3ax(x-2) (2)x(x2)xx(x+1) (3)x24xax4a(x-4)(x-a) (4)25x249(5x-9)(5x+9) (5)36x260x25(6x-5)2 (6)4x212x9(2x+3)2 (7)x29x18(x-3)(x-6) (8)2x25x3(x-3)(2x+1) (9)12x250x82(6x-1)(x-4) 40.因式分解(x2)(x3)(x2)(x4)(x+2)(2x-1) 41.因式分解2ax23x2ax3 (x+1)(2ax-3) 42.因式分解9x266x121(3x-11)2 43.因式分解82x22(2+x)(2-x) 44.因式分解x2
4、x14 整数内无法分解 45.因式分解9x230x25(3x-5)2 46.因式分解20x29x20(-4x+5)(5x+4) 47.因式分解12x229x15(4x-3)(3x-5) 48.因式分解36x239x93(3x+1)(4x+3) 49.因式分解21x231x22(21x+11)(x-2) 50.因式分解9x435x24(9x2+1)(x+2)(x-2) 51.因式分解(2x1)(x1)(2x1)(x3)2(x-1)(2x+1) 52.因式分解2ax23x2ax3(x+1)(2ax-3) 53.因式分解x(y2)xy1(x-1)(y+1) 54.因式分解(x23x)(x3)2(x-
5、3)(2x-3) 55.因式分解9x266x121(3x-11)2 56.因式分解82x22(2-x)(2+x) 57.因式分解x41(x-1)(x+1)(x2+1) 58.因式分解x24xxy2y4(x+2)(x-y+2) 59.因式分解4x212x5(2x-1)(2x-5) 60.因式分解21x231x22(21x+11)(x-2) 61.因式分解4x24xyy24x2y3(2x+y-3)(2x+y+1) 62.因式分解9x535x34xx(9x2+1)(x+2)(x-2) 63.因式分解下列各式: (1)3x26x3x(x-2) (2)49x225(7x+5)(7x-5) (3)6x21
6、3x5(2x-1)(3x-5) (4)x223x(x-1)(x-2) (5)12x223x24(3x-8)(4x+3) (6)(x6)(x6)(x6)(x-6)(x+5) (7)3(x2)(x5)(x2)(x3)2(x-6)(x+2) (8)9x242x49(3x+7)2 。1若(2x)n81 = (4x2+9)(2x+3)(2x3),那么n的值是( B ) A2 B 4 C6 D8 2若9x212xy+m是两数和的平方式,那么m的值是( B ) A2y2 B4y 2 C4y2 D16y2 3把多项式a4 2a2b2+b4因式分解的结果为( D ) Aa2(a22b2)+b4 B(a2b2)2
7、 C(ab)4 D(a+b)2(ab)2 4把(a+b)24(a2b2)+4(ab)2分解因式为( C ) A( 3ab)2 B(3b+a)2 C(3ba)2 D( 3a+b)2 6已知x,y为任意有理数,记M = x2+y2,N = 2xy,则M与N的大小关系为( B ) AMN BMN CMN D不能确定 7对于任何整数m,多项式( 4m+5)29都能( A )A被8整除 B被m整除 C被(m1)整除 D被(2n1)整除 9下列变形中,是正确的因式分解的是( D ) A 0.09m2 n2 = ( 0.03m+ n )( 0.03mn) Bx210 = x291 = (x+3)(x3)1
8、Cx4x2 = (x2+x)(x2x) D(x+a)2(xa)2 = 4ax 10多项式(x+yz)(xy+z)(y+zx)(zxy)的公因式是( A ) Ax+yz Bxy+z Cy+zx D不存在 11已知x为任意有理数,则多项式x1x2的值( ) A一定为负数 B不可能为正数 C一定为正数 D可能为正数或负数或零 二、解答题: 分解因式: (1)(ab+b)2(a+b)2 (2)(a2x2)24ax(xa)2 (3)7xn+114xn+7xn1(n为不小于1的整数) 答案: 一、选择题: 1B 说明:右边进行整式乘法后得16x481 = (2x)481,所以n应为4,答案为B 2B 说明
9、:因为9x212xy+m是两数和的平方式,所以可设9x212xy+m = (ax+by)2,则有9x212xy+m = a2x2+2abxy+b2y2,即a2 = 9,2ab = 12,b2y2 = m;得到a = 3,b = 2;或a = 3,b = 2;此时b2 = 4,因此,m = b2y2 = 4y2,答案为B 3D 说明:先运用完全平方公式,a4 2a2b2+b4 = (a2b2)2,再运用两数和的平方公式,两数分别是a2、b2,则有(a2b2)2 = (a+b)2(ab)2,在这里,注意因式分解要分解到不能分解为止;答案为D 4C 说明:(a+b)24(a2b2)+4(ab)2 =
10、 (a+b)22(a+b)2(ab)+2(ab)2 = a+b2(ab)2 = (3ba)2;所以答案为C 6B 说明:因为MN = x2+y22xy = (xy)20,所以MN 7A 说明:( 4m+5)29 = ( 4m+5+3)( 4m+53) = ( 4m+8)( 4m+2) = 8(m+2)( 2m+1) 9D 说明:选项A,0.09 = 0.32,则 0.09m2 n2 = ( 0.3m+n)( 0.3mn),所以A错;选项B的右边不是乘积的形式;选项C右边(x2+x)(x2x)可继续分解为x2(x+1)(x1);所以答案为D 10A 说明:本题的关键是符号的变化:zxy = (x
11、+yz),而xy+zy+zx,同时xy+z(y+zx),所以公因式为x+yz 11B 说明:x1x2 = (1x+x2) = (1x)20,即多项式x1x2的值为非正数,正确答案应该是B 二、解答题: (1) 答案:a(b1)(ab+2b+a) 说明:(ab+b)2(a+b)2 = (ab+b+a+b)(ab+bab) = (ab+2b+a)(aba) = a(b1)(ab+2b+a) (2) 答案:(xa)4 说明:(a2x2)24ax(xa)2 = (a+x)(ax)24ax(xa)2 = (a+x)2(ax)24ax(xa)2 = (xa)2(a+x)24ax = (xa)2(a2+2a
12、x+x24ax) = (xa)2(xa)2 = (xa)4 (3) 答案:7xn1(x1)2 说明:原式 = 7xn1 x27xn1 2x+7xn1 = 7xn1(x22x+1) = 7xn1(x1)2因式分解之十字相乘法专项练习题(1)a27a+6; (2)8x2+6x35;(3)18x221x+5; (4) 209y20y2;(5)2x2+3x+1; (6)2y2+y6; (7)6x213x+6; (8)3a27a6; (9)6x211x+3; (10)4m2+8m+3; (11)10x221x+2; (12)8m222m+15; (13)4n2+4n15; (14)6a2+a35; (15)5x28x13; (16)4x2+15x+9; (17)15x2+x2; (18)6y2+19y+10; (19) 2