求含参二次函数因式分解技巧 求初中因式分解题目30道 二次函数题目20道， 简单就可以了...
\u4e8c\u6b21\u51fd\u6570\u4e2d\u7684\u56e0\u5f0f\u5206\u89e3\u95ee\u9898\u4e8c\u6b21\u51fd\u6570y=ax²+bx+c\u5bf9\u5e94\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u6240\u8c13\u7684\u4e0d\u80fd\u56e0\u5f0f\u5206\u89e3\u5e94\u8be5\u6709\u51e0\u79cd\u60c5\u51b5\uff0c\u4e00\u662f\u5bf9\u5e94\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u5224\u522b\u5f0f\u5c0f\u4e8e0\uff0c\u8fd9\u65f6\u5b83\u4e0eX\u8f74\u6ca1\u6709\u5b9e\u4ea4\u70b9\uff1b\u4e8c\u662f\u5bf9\u5e94\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u5224\u522b\u5f0f\u5927\u4e8e\u7b49\u4e8e0\uff0c\u4f46\u6ca1\u6709\u6709\u7406\u6839\uff0c\u8fd9\u65f6\u53ef\u7528\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u6c42\u6839\u516c\u5f0f\u6765\u89e3\uff0c\u516c\u5f0f\u662fx=[-b\u00b1\u221a(b²-4ac)]/(2a)\u3002\u9876\u70b9\u7eb5\u5750\u6807\u4e3a(4ac-b²)/(4a)\uff0c\u5f53a>0\u5f00\u53e3\u5411\u4e0a\u65f6\u662f\u6700\u5c0f\u503c\uff0c\u53cd\u4e4b\u662f\u6700\u5927\u503c\u3002
1\uff0e\u4e00\u4e2a\u591a\u9879\u5f0f\u82e5\u80fd\u56e0\u5f0f\u5206\u89e3\uff0c\u5219\u8fd9\u4e2a\u591a\u9879\u5f0f\u88ab\u5176\u4efb\u4e00\u56e0\u5f0f\u9664\u6240\u5f97\u4f59\u5f0f\u4e3a_________\uff0e
2\uff0e\u53d8\u5f62\uff081\uff09(a+b)(a-b)=a2-b2\uff0c\uff082\uff09a2-b2=(a-b)(a+b)\u4e2d\uff0c\u5c5e\u4e8e\u56e0\u5f0f\u5206\u89e3\u8fc7\u7a0b\u7684\u662f________\uff0e
3\uff0e\u82e5a\uff0cb\uff0cc\u4e09\u6570\u4e2d\u6709\u4e24\u6570\u76f8\u7b49\uff0c\u5219
a2(b-c)+b2(c-a)+c2(a-b)\u7684\u503c\u4e3a_________\uff0e
4\uff0e12.718\u00d70.125-0.125\u00d74.718=_________\uff0e
5\uff0e1.13\u00d72.5+2.25\u00d72.5+0.62\u00d72.5=_________\uff0e
6\uff0e\u5206\u89e3\u56e0\u5f0f\uff1aa2(b2-c2)-c2(b-c)(a+b)=_________\uff0e
7\uff0e\u56e0\u5f0f\u5206\u89e3\uff1a(a-2b)(3a+4b)+(2a-4b)(2a-3b)=(a-2b)•( )\uff0e
8\uff0e\u82e5a+b+c=m\uff0c\u5219\u6574\u5f0fm•[(a-b)2+(b-c)2+(c-a)2]+6(a+b+c)(ab+bc+ca)\u53ef\u7528m\u8868\u793a\u4e3a_______________\uff0e
9\uff0e(2x+1)y2+(2x+1)2y=_________\uff0e
10\uff0e\u56e0\u5f0f\u5206\u89e3\uff1a(x-y)n-(x-y)n-2=(x-y)n-2•_________\uff0e
11\uff0em(a-m)(a-n)-n(m-a)(a-n)=_________\uff0e
12\uff0e\u56e0\u5f0f\u5206\u89e3\uff1ax(m-n)+(n-m)y-z(m-n)=(m-n)( )\uff0e
13\uff0e\u56e0\u5f0f\u5206\u89e3\uff1a
(x+2y)(3x2-4y2)-(x+2y)2(x-2y)=________\uff0e
14\uff0e21a3b-35a2b3=_________\uff0e
15\uff0e3x2yz+15xz2-9xy2z=__________\uff0e
16\uff0ex2-2xy-35y2=(x-7y)( )\uff0e
17\uff0e2x2-7x-15=(x-5)( )\uff0e
18\uff0e20x2-43xy+14y2=(4x-7y)( )\uff0e
19\uff0e18x2-19x+5=( )(2x-1)\uff0e
20\uff0e6x2-13x+6=( )( )\uff0e
21\uff0e5x2+4xy-28y2=( )( )\uff0e
22\uff0e-35m2n2+11mn+6=-( )( )\uff0e
23\uff0e6+11a-35a2=( )( )\uff0e
24\uff0e6-11a-35a2=( )( )\uff0e
25\uff0e-1+y+20y2=( )( )\uff0e
26\uff0e20x2+( )+14y2=(4x-7y)(5x-2y)\uff0e
27\uff0ex2-3xy-( )=(x-7y)(x+4y)\uff0e
28\uff0ex2+( )-28y2=(x+7y)(x-4y)\uff0e
29\uff0ex2+( )-21y2=(x-7y)(x+3y)\uff0e
30\uff0ekx2+5x-6=(3x-2)( )\uff0ck=______\uff0e
31\uff0e6x2+5x-k=(3x-2)( )\uff0ck=______\uff0e
32\uff0e6x2+kx-6=(3x-2)( )\uff0ck=______\uff0e
33\uff0e18x2-19x+5=(9x+m)(2x+n)\uff0c\u5219m=_____\uff0cn=_____\uff0e
34\uff0e18x2+19x+m=(9x+5)(2x+n)\uff0c\u5219m=_____\uff0cn=_____\uff0e
35\uff0e20x2-43xy+14y2=(4x+m)(5x+n)\uff0c\u5219m=_____\uff0cn=_____\uff0e
36\uff0e20x2-43xy+m=(4x-7y)(5x+n)\uff0c\u5219m=_____\uff0cn=_____\uff0e
38\uff0ex4-4x3+4x2-1=_______\uff0e
39\uff0e2x2-3x-6xy+9y=________\uff0e
40\uff0e21a2x-9ax2+6xy2-14ay2=________\uff0e
41\uff0ea3+a2b+a2c+abc=________\uff0e
42\uff0e2(a2-3ac)+a(4b-3c)=_________\uff0e
43\uff0e27x3+54x2y+36xy2+8y3_______\uff0e
44\uff0e1-3(x-y)+3(x-y)2-(x-y)3=_______\uff0e
45\uff0e(x+y)2+(x+m)2-(m+n)2-(y+n)2=_______\uff0e
46\uff0e25x2-4a2+12ab-9b2=_______\uff0e
47\uff0ea2-c2+2ab+b2-d2-2cd=_______\uff0e
48\uff0ex4+2x2+1-x2-2ax-a2=________\uff0e
50\uff0ea2-4b2-4c2-8bc=__________\uff0e
51\uff0ea2+b2+4a-4b-2ab+4=________\uff0e
52\uff0ex2+2x-3\u56e0\u5f0f\u5206\u89e3\u5f97[ ]
A\uff0e(x+1)2-4\uff1b B\uff0ex(x+2)-3\uff1b
C\uff0e(x-1)(x+3)\uff1b D\uff0e(x-2)(x+2)+(2x+1)\uff0e
53\uff0ea3-b3\u56e0\u5f0f\u5206\u89e3\u5f97[ ]
A\uff0e(a-b)(a2+ab+b2)\uff1b B\uff0e(a+b)(a2-ab+b2)\uff1b
C\uff0e(a-b)(a2-ab+b2)\uff1b D\uff0e(a+b)(a2+ab+b2)\uff0e
54\uff0ea2+b2+c2+2ab+2bc+2ac\u56e0\u5f0f\u5206\u89e3\u5f97[ ]
A\uff0e(a+b)2+c(c+2a+2b)\uff1b B\uff0e(a+b+c)2\uff1b
C\uff0e(b+c)2+a2+2a(b+c)\uff1b D\uff0e(a+b)2+(b+c)2+(c+a)2\uff0e
55\uff0ex2-2ax+a2\u56e0\u5f0f\u5206\u89e3\u5f97[ ]
A\uff0e(x-a)2 B\uff0ex(x-2a)+a2
C\uff0e(x2-a2)-2a(x-a)\uff1b D\uff0ex(x-a)-a(x-a)\uff0e
56\uff0e(-2)m+2(-2)m-1\u7684\u503c\u662f[ ]
A\uff0e1\uff1b B\uff0e-1\uff1b
C\uff0e0\uff1b D\uff0e(-1)m+1\uff0e
57\uff0e2y(x-y)2-(y-x)3= [ ]
A\uff0e(x+y)(x-y)2\uff1b B\uff0e(3y-x)(x-y)2\uff1b
C\uff0e(x-3y)(y-x)2\uff1b D\uff0e(y-x)3\uff0e
58\uff0e-28a2b+21ab2-7ab=[ ]
A\uff0e7ab(4a-3b+1)\uff1b B\uff0e7ab(-4a-3b-1)\uff1b
C\uff0e-7ab(4a-3b+1)\uff1b D\uff0e-7ab(4a-3b)\uff0e
59\uff0e-6x2+9xy-3x= [ ]
A\uff0e3x(2x-3y+1)\uff1b B\uff0e-3x(2x-3y)\uff1b
C\uff0e-3x(2x+3y-1)\uff1b D\uff0e-3x(2x-3y+1)\uff0e
60\uff0e(x+y-z)(x-y+z)+(y-x+z)(y-x-z)= [ ]
A\uff0e2(y-z)(y-x+z)\uff1b B\uff0e2x(x-y+z)\uff1b
C\uff0e2y(x-y+z)\uff1b D\uff0e2(x-z)(x-y+z)\uff0e
61\uff0e3m(x-y)-2(y-x)2=[ ]
A\uff0e(x-y)(3m+2x-2y)\uff1b B\uff0e(x-y)(3m-2x+2y)\uff1b
C\uff0e(y-x)(2y-2x+3m)\uff1b D\uff0e(y-x)(2x-2y+3m)\uff0e
62\uff0em(m-x)(m-y)-y(x-m)(y-m)= [ ]
A\uff0e(x-m)(m-y)(m+y)\uff1b B\uff0e(m-x)(m-y)(m+y)\uff1b
C\uff0e(m-x)(m-y)2\uff1b D\uff0e(x-m)(m-y)2\uff0e
63\uff0e4a(x-y)2-2b(y-x)2+(y-x)=[ ]
A\uff0e(x-y)(4ax-4ay-2bx+2by-1)\uff1b
B\uff0e(x-y)(4ax-4ay+2bx-2by-1)\uff1b
C\uff0e(y-x)(4ax-4ay+2bx-2by+1)\uff1b
D\uff0e(y-x)(4ay-4ax-2by+2bx)\uff0e
64\uff0e(x-y)(a-b)-(y-x)2+(y-x)=[ ]
A\uff0e(x-y)(x-y+a-b-1)\uff1b B\uff0e(x-y)(a-b-x-y-1)\uff1b
C\uff0e(x-y)(y-x+a-b-1)\uff1b D\uff0e(x-y)(y-x+a-b)\uff0e
65\uff0e-4a3+16a2+12a\u5728\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u5e94\u63d0\u53d6\u7684\u516c\u56e0\u5f0f\u662f[ ]
A\uff0e4a3\uff1b B\uff0e4a2\uff1b
C\uff0e-4a2\uff1b D\uff0e-4a\uff0e
66\uff0e49x3yz3+14x2y2z2-21xy2z2\u5728\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u5e94\u63d0\u53d6\u7684\u516c\u56e0\u5f0f\u662f[ ]
A\uff0e7x3yz3\uff1b B\uff0e7x2y2z2\uff1b
C\uff0e7xy2z2\uff1b D\uff0e7xyz2\uff0e
67\uff0e\u5206\u89e3\u56e0\u5f0f6a(a-b)2-8(a-b)3\u65f6\uff0c\u5e94\u63d0\u53d6\u7684\u516c\u56e0\u5f0f\u662f[ ]
A\uff0ea\uff1b B\uff0e6a(a-b)2\uff1b
C\uff0e8a(a-b)\uff1b D\uff0e2(a-b)2\uff0e
68\uff0e\u89c2\u5bdf\u4e0b\u5217\u4ee3\u6570\u5f0f\uff1a
\uff081\uff092a+b\u548ca+b\uff1b \uff082\uff095m(a-b)\u548c-a+b\uff1b
\uff083\uff093(a+b)\u548c-a-b\uff1b \uff084\uff09x3-y3\u548cx2-xy+y2\uff0e
\u5176\u4e2d\uff0c\u6709\u516c\u56e0\u5f0f\u7684\u53ea\u6709[ ]
A\uff0e\uff081\uff09\uff0c\uff082\uff09\uff1b B\uff0e\uff082\uff09\uff0c\uff083\uff09\uff1b
C\uff0e\uff083\uff09\uff0c\uff084\uff09\uff1b D\uff0e\uff081\uff09\uff0c\uff084\uff09\uff0e
69\uff0e\u5206\u89e3\u56e0\u5f0f\uff1a(a-b)(a2-ab+b2)-ab(b-a)\u4e3a[ ]
A\uff0e(a-b)(a2+b2)\uff1b B\uff0e(a-b)2(a+b)\uff1b
C\uff0e(a-b)3\uff1b D\uff0e(a-b)+a2+b2\uff0e
70\uff0e\u591a\u9879\u5f0f0.5x(a-b)-0.25y(b-a)\u4e2d\uff0c\u53ef\u63d0\u53d6\u7684\u516c\u56e0\u5f0f\u4e3a[ ]
A\uff0e0.5x-0.25y\uff1b B\uff0e0.5x+0.25y\uff1b
C\uff0ea-b\uff1b D\uff0e0.25(a-b)\uff0e
71\uff0e\u5728\u591a\u9879\u5f0f9xyz-6xy2z+3xz2\u4e2d\uff0c\u53ef\u63d0\u53d6\u7684\u516c\u56e0\u5f0f\u4e3a[ ]
A\uff0exyz\uff1b B\uff0e3x\uff1b
C\uff0e3xz\uff1b D\uff0e3xy\uff0e
72\uff0e\u591a\u9879\u5f0f-a(a-x)(x-b)+ab(a-x)(b-x)\u4e2d\uff0c\u53ef\u63d0\u53d6\u7684\u516c\u56e0\u5f0f\u4e3a[ ]
A\uff0ea(a-x)\uff1b B\uff0ea(x-a)(x-b)\uff1b
C\uff0e(a-x)(x-b)\uff1b D\uff0e-a(x-a)\uff0e
73\uff0e\u591a\u9879\u5f0f8x3y2-12x2y3-4x2y2\uff0c6m2bx2-9m2bxy-3m2bx\u548c-10mx4y2+15mx3y3+5mx3y2\u7684\u6b21\u6570\u6700\u9ad8\u7684\u516c\u56e0\u5f0f\u662f[ ]
A\uff0ex\uff1b B\uff0exy\uff1b
C\uff0ex(2x-3y-1)\uff1b D\uff0emx(2x-3y-1)\uff0e
74\uff0e\u89c2\u5bdf\u4e0b\u5217\u591a\u9879\u5f0f\uff1a
\uff081\uff092a2b+4b2\uff1b
\uff082\uff09(a+b)2x-5x2(a+b)+4(a-b)2\uff1b
\uff083\uff099a2(x-y)-4b(y-x)\uff1b
\uff084\uff098a3-4a2+2a-1\uff0e
\u5176\u4e2d\uff0c\u53ef\u4ee5\u7528\u63d0\u516c\u56e0\u5f0f\u6cd5\u5206\u89e3\u56e0\u5f0f\u7684\u53ea\u6709[ ]
A\uff0e\uff081\uff09\uff0c\uff084\uff09\uff1b B\uff0e\uff082\uff09\uff0c\uff083\uff09\uff1b
C\uff0e\uff082\uff09\uff0c\uff084\uff09\uff1b D\uff0e\uff081\uff09\uff0c\uff083\uff09\uff0e
75\uff0e(m-n)3-(2n-m)3\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e-3n(m2+3n3-2mn)\uff1b B\uff0en(m2+2mn-3n2)\uff1b
C\uff0e(2m-3n)(m2-3mn+3n2)\uff1b D\uff0e(n-2m)(m2+2mn+3n2)\uff0e
76\uff0e(m-n)3+(2m-3n)3\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(3m-4n)(3m2+7n2-9mn)\uff1b B\uff0e(2m-n)(3m2+7n2+9mn)\uff1b
C\uff0e(3m+4n)(3m2+7n2-9mn)\uff1b D\uff0e(3m-4n)(3m2+9mn+7n2)\uff0e
77\uff0e4m2-n2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(2m-n)(2m+n)\uff1b B\uff0e(n-2m)(n+2m)\uff1b
C\uff0e(2m-n)2\uff1b D\uff0e(4m-n)(4m+n)\uff0e
78\uff0e144a2-256b2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(12a+16b)(12a+16b)\uff1b B\uff0e(12a-16b)2\uff1b
C\uff0e(12a-26b)(12a+26b)\uff1b D\uff0e16(3a-4b)(3a+4b)\uff0e
79\uff0e16x16-y4z4\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(2x4-yz)(2x4+yz)(4x8+y2z2)\uff1b B\uff0e(2x2-yz)(2x2+yz)(4x4+y2z2)\uff1b
C\uff0e(4x2-yz)(4x2+yz)(4x4+y2z2)\uff1b D\uff0e(4x4-yz)(4x4+yz)(x4+y2z2)\uff0e
80\uff0e81x8-225a4b6\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(9x4-25a2b4)(9x4-25a2b2)\uff1b B\uff0e(9x2-25a2b3)(9x4-25a2b3)\uff1b
C\uff0e(9x2-15a2b3)(9x4+15a4b3)\uff1b D\uff0e(9x4-15a2b3)(9x4+15a2b3)\uff0e
81\uff0e25a2b4c16-1\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(5abc-1)(5abc+1)\uff1b B\uff0e(6ab2c4-1)(5ab2c4+1)\uff1b
C\uff0e(5ab2c8-1)(5ab2c8+1)\uff1b D\uff0e(5abc4-1)(5abc4+1)\uff0e
82\uff0e(a+b)2-100\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(a+b-10)(a-b+10)\uff1b B\uff0e(a+b-10)(a+b+10)\uff1b
C\uff0e(a+b-10)2\uff1b D\uff0e(a+b+10)2\uff0e
83\uff0e289-(ax-by)2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(17-ax-by)(17+ax+by)\uff1b
B\uff0e(17-ax-by)(17+ax-by)\uff1b
C\uff0e(17-ax+by)(17+ax+by)\uff1b
D\uff0e(17-ax+by)(17+ax-by)\uff0e
84\uff0e361-(3a+2b)2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(19-3a-2b)(19+3a+2b)\uff1b
B\uff0e(19-3a+2b)(19+3a-2b)\uff1b
C\uff0e(19+3a-2b)(19-3a+2b)\uff1b
D\uff0e(3a+2b-19)(3a-2b+19)\uff0e
[ ]
86\uff0e(a-b)4-81b4\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(a-4b)(a+2b)(a2-2ab+10b2)\uff1b
B\uff0e(a-4b)(a+2b)(a-5b)(a+3b)\uff1b
C\uff0e(a2-2ab-8b2)(a2-2ab+10b2)\uff1b
D\uff0e(a2-2ab+8b2)(a2-2ab+10b2)\uff0e
87\uff0e(a+b)2-4(a-b)2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(a+b-2a-2b)(a+b+2a-b)\uff1b
B\uff0e(5a-3b)(5b-3a)\uff1b
C\uff0e(3a-b)(3b-a)\uff1b
D\uff0e(3a-b)(2b-a)\uff1b\uff0e
88\uff0eb2-(a-b+c)2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(b+a+b+c)(b-a+b-c)\uff1b
B\uff0e(b+a-b+c)(2b+a+c)\uff1b
C\uff0e(a+c)(2b-a+c)\uff1b
D\uff0e(a+c)(2b-a-c)\uff0e
[ ]
90\uff0e64a8-b2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(64a4-b)(a4+b)\uff1b B\uff0e(16a2-b)(4a2+b)\uff1b
C\uff0e(8a4-b)(8a4+b)\uff1b D\uff0e(8a2-b)(8a4+b)\uff0e
91\uff0e(a+2b)2-(x-3y)2\u56e0\u5f0f\u5206\u89e3\u4e3a[ ]
A\uff0e(a+2b+x-3y)(a+2b-x-3y)\uff1b
B\uff0e(a+2b+x+3y)(a+2b-x-3y)\uff1b
C\uff0e(a+2b+x-3y)(a+2b-x+3y)\uff1b
x^+ax+a^/4-(a^/4 +b)
(x+a/2)^-(√(a^/4 +b))^
(x+a/2+√(a^/4 +b))(x+a/2-√(a^/4 +b))
万能公式因式分解
例子
x^+7x-8
=x^+7x+(7/2)^-((7/2)^+8)
=(x+7/2)^-(9/2)^
=(x+7/2+9/2)(x+7/2-9/2)
=(x+8)(x-1)
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