\u5728\u5e73\u5e38\u751f\u6d3b\u4e2d\u6211\u4eec\u901a\u5e38\u4f1a\u770b\u5230\u6709\u4e9b\u5b69\u5b50\u8ba1\u7b97\u7279\u522b\u5feb\uff0c\u522b\u4eba\u8fd8\u6ca1\u52a8\u7b14\uff0c\u6709\u4e9b\u5b69\u5b50\u5df2\u7ecf\u7b97\u51fa\u6765\u4e86\u3002\u5176\u4e2d\u7ed9\u4e00\u4e2a\u8bc0\u7a8d\u5c31\u662f\u7528\u4e86\u5341\u5b57\u76f8\u4e58\u6cd5\uff0c\u5b83\u4e0d\u662f\u5f88\u96be\uff0c\u4f46\u662f\uff0c\u60f3\u8981\u505a\u7684\u5feb\u53c8\u51c6\uff0c\u8fd8\u5f97\u9700\u8981\u591a\u52a0\u7ec3\u4e60\uff0c\u5f88\u591a\u4e1c\u897f\u662f\u53ea\u53ef\u610f\u4f1a\u4e0d\u80fd\u8a00\u4f20\u7684\u3002<\/p>\n
\u5341\u5b57\u76f8\u4e58\u6cd5\u516c\u5f0f\u6280\u5de7<\/p>\n
1\u3001 \u4e8c\u6b21\u9879\u7cfb\u6570\u4e3a1\u7684\u5341\u5b57\u76f8\u4e58<\/p>\n
\u6b64\u7c7b\u56e0\u5f0f\u5206\u89e3\u7684\u6a21\u578b\u4e3ax2+\uff08a+b\uff09x+ab=\uff08x+a\uff09\uff08x+b\uff09<\/p>\n
1.×2+6x+8 2.×2-6x+8 3.×2+2x-8 4.×2-2x-8<\/p>\n
=\uff08x+2\uff09\uff08x+4\uff09 =\uff08x-2\uff09\uff08x-4\uff09 =\uff08x-2\uff09\uff08x+4\uff09 =\uff08x+2\uff09\uff08x-4\uff09<\/p>\n
\u57fa\u672c\u539f\u7406\uff1a\u5de6\u5217\u76f8\u4e58\u7684\u79ef\u4e3a\u4e8c\u6b21\u9879\uff0c\u53f3\u5217\u76f8\u4e58\u7684\u79ef\u4e3a\u5e38\u6570\u9879\uff0c\u4ea4\u53c9\u76f8\u4e58\u7684\u79ef\u7684\u548c\u4e3a\u4e00\u6b21\u9879\u3002<\/p>\n
\u5f15\u7533\uff1a\u5982\u679c\u4e8c\u6b21\u9879\u7cfb\u6570\u4e3a\u8d1f\u6570\uff0c\u5148\u628a\u4e8c\u6b21\u9879\u7cfb\u6570\u8f6c\u6362\u4e3a\u6b63\u6570\uff0c\u7136\u540e\u770b\u5e38\u6570\u9879\u7cfb\u6570\u548c\u4e00\u6b21\u9879\u7cfb\u6570\u3002<\/p>\n
\u5982\u679c\u5e38\u6570\u9879\u7cfb\u6570\u4e3a\u6b63\uff0c\u4e00\u6b21\u9879\u7cfb\u6570\u4e3a\u6b63\uff0c\u5219\u62c6\u4e3a\u4e24\u4e2a\u6b63\u6570\u76f8\u4e58\u3002<\/p>\n
\u5982\u679c\u5e38\u6570\u9879\u7cfb\u6570\u4e3a\u6b63\uff0c\u4e00\u6b21\u9879\u7cfb\u6570\u4e3a\u8d1f\uff0c\u5219\u62c6\u4e3a\u4e24\u4e2a\u8d1f\u6570\u76f8\u4e58\u3002<\/p>\n
\u5982\u679c\u5e38\u6570\u9879\u7cfb\u6570\u4e3a\u8d1f\uff0c\u4e00\u6b21\u9879\u7cfb\u6570\u4e3a\u6b63\uff0c\u5219\u62c6\u4e3a\u4e00\u6b63\u4e00\u8d1f\u76f8\u4e58\uff0c\u5e76\u4e14\u6b63\u6570\u7684\u7edd\u5bf9\u503c\u5927\u3002<\/p>\n
\u5982\u679c\u5e38\u6570\u9879\u7cfb\u6570\u4e3a\u8d1f\uff0c\u4e00\u6b21\u9879\u7cfb\u6570\u4e3a\u8d1f\uff0c\u5219\u62c6\u4e3a\u4e00\u6b63\u4e00\u8d1f\u76f8\u4e58\u3002\u5e76\u4e14\u8d1f\u6570\u7684\u7edd\u5bf9\u503c\u5927\u3002<\/p>\n
2\u3001 \u4e8c\u6b21\u9879\u7cfb\u6570\u4e0d\u4e3a1\u7684\u5341\u5b57\u76f8\u4e58<\/p>\n
\u6b64\u7c7b\u578b\u539f\u7406\u4e0e\u4e0a\u4e2a\u7c7b\u578b\u4e00\u6837\uff0c\u53ea\u4e0d\u8fc7\u628a\u4e8c\u6b21\u9879\u7cfb\u6570\u4e5f\u5f97\u62c6\u4e3a\u4e24\u4e2a\u6b63\u6570\u76f8\u4e58\u3002<\/p>\n
\u6b64\u7c7b\u56e0\u5f0f\u5206\u89e3\u7684\u6a21\u578b\u4e3aabx2+\uff08ad+bc\uff09x+cd=\uff08ax+c\uff09\uff08bx+d\uff09<\/p>\n
\u4e3e\u4f8b\u8bf4\u660e\uff1a2×2+13x+15=\uff082x+3\uff09\uff08x+5\uff09<\/p>\n
\u5176\u4e2d2x\u4e0ex\u7684\u79ef\u4e3a\u4e8c\u6b21\u98792×2 \uff0c3\u4e0e5\u7684\u79ef\u4e3a\u5e38\u6570\u9879\uff0c2x\u4e0e5\u7684\u79ef\u52a0\u4e0ax\u4e0e3\u7684\u79ef\u4e4b\u548c\u4e3a\u4e00\u6b21\u9879\u3002<\/p>\n
3\u3001 \u53cc\u5341\u5b57\u76f8\u4e58\u6cd5<\/p>\n
\u6b64\u7c7b\u578b\u539f\u7406\u4e0d\u53d8\uff0c\u53ea\u662f\u75282\u6b21\u5341\u5b57\u76f8\u4e58\uff0c\u5e94\u7528\u6574\u4f53\u601d\u60f3\u3002\u90a3\u4e48\u75282×2-7xy-22y2-5x+35y-3 \u6765\u8bf4\u660e\u53cc\u5341\u5b57\u65b9\u6cd5\u7684\u5e94\u7528\u3002<\/p>\n
\u7b2c\u4e00\u79cd\u65b9\u6cd5\uff1a<\/p>\n
\u53ef\u4ee5\u628ax\u5f53\u4e3b\u5143\uff0c\u7528\u6574\u7406\u601d\u60f3\u6765\u5206\u89e3\uff0c\u5177\u4f53\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/p>\n
2×2-7xy-22y2-5x+35y-3 = 2×2+\uff087y+5\uff09x -22y2+35y-3<\/p>\n
\u7136\u540e\u5148\u5c06-22y2+35y-3\u5206\u89e3\u4e3a \u2013\uff082y-3\uff09\uff0811y-1\uff09 =\uff082y-3\uff09\uff08-11y+1\uff09<\/p>\n
\u7136\u540e\u7528\u6574\u4f53\u601d\u60f3\u6765\u5206\u89e3\uff0c\u628a\uff082y-3\uff09 \u548c\uff08-11y+1\uff09\u770b\u62102\u4e2a\u6574\u4f53\u3002<\/p>\n
2×2-7xy-22y2-5x+35y-3 = 2×2-\uff087y+5\uff09x -22y2+35y-3<\/p>\n
=2×2-\uff087y+5\uff09x+\uff082y-3\uff09\uff08-11y+1\uff09 =[x+\uff082y-3\uff09][2x+\uff08-11y+1\uff09]<\/p>\n
=\uff08x+2y-3\uff09\uff082x-11y+1\uff09<\/p>\n
\u7b2c\u4e8c\u79cd\u65b9\u6cd5\uff1a<\/p>\n
\u53ef\u4ee5\u5148\u5206\u89e3\u4e8c\u6b21\u98792×2-7xy-22y2 =\uff08x+2y\uff09\uff082x-11y\uff09<\/p>\n
\u7136\u540e\u7528\u6574\u4f53\u601d\u60f3\u6765\u5206\u89e3\uff0c\u628a\uff08x+2y\uff09\u548c\uff082x-11y\uff09\u770b\u62102\u4e2a\u6574\u4f53\u3002<\/p>\n
2×2-7xy-22y2-5x+35y-3 = \uff08x+2y\uff09\uff082x-11y\uff09 -5x+35y-3<\/p>\n
==\uff08x+2y-3\uff09\uff082x-11y+1\uff09<\/p>\n
\u5341\u5b57\u76f8\u4e58\u6cd5\u6982\u5ff5<\/p>\n
\u5341\u5b57\u5206\u89e3\u6cd5\u7684\u65b9\u6cd5\u7b80\u5355\u6765\u8bb2\u5c31\u662f\uff1a\u5341\u5b57\u5de6\u8fb9\u76f8\u4e58\u7b49\u4e8e\u4e8c\u6b21\u9879\u7cfb\u6570\uff0c\u53f3\u8fb9\u76f8\u4e58\u7b49\u4e8e\u5e38\u6570\u9879\uff0c\u4ea4\u53c9\u76f8\u4e58\u518d\u76f8\u52a0\u7b49\u4e8e\u4e00\u6b21\u9879\u7cfb\u6570\u3002\u5176\u5b9e\u5c31\u662f\u8fd0\u7528\u4e58\u6cd5\u516c\u5f0f\uff08x+a\uff09\uff08x+b\uff09=x2+\uff08a+b\uff09x+ab\u7684\u9006\u8fd0\u7b97\u6765\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<\/p>\n
\u5341\u5b57\u5206\u89e3\u6cd5\u80fd\u7528\u4e8e\u4e8c\u6b21\u4e09\u9879\u5f0f\uff08\u4e00\u5143\u4e8c\u6b21\u5f0f\uff09\u7684\u5206\u89e3\u56e0\u5f0f\uff08\u4e0d\u4e00\u5b9a\u662f\u6574\u6570\u8303\u56f4\u5185\uff09\u3002\u5bf9\u4e8e\u50cfax?+bx+c=\uff08a1x+c1\uff09\uff08a2x+c2\uff09\u8fd9\u6837\u7684\u6574\u5f0f\u6765\u8bf4\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u7684\u5173\u952e\u662f\u628a\u4e8c\u6b21\u9879\u7cfb\u6570a\u5206\u89e3\u6210\u4e24\u4e2a\u56e0\u6570a1\uff0ca2\u7684\u79ef\uff0c\u628a\u5e38\u6570\u9879c\u5206\u89e3\u6210\u4e24\u4e2a\u56e0\u6570c1\uff0cc2\u7684\u79ef\uff0c\u5e76\u4f7fa1c2+a2c1\u6b63\u597d\u7b49\u4e8e\u4e00\u6b21\u9879\u7684\u7cfb\u6570b\u3002\u90a3\u4e48\u53ef\u4ee5\u76f4\u63a5\u5199\u6210\u7ed3\u679c\uff1aax?+bx+c=\uff08a1x+c1\uff09\uff08a2x+c2\uff09\u3002\u5728\u8fd0\u7528\u8fd9\u79cd\u65b9\u6cd5\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u8981\u6ce8\u610f\u89c2\u5bdf\uff0c\u5c1d\u8bd5\uff0c\u5e76\u4f53\u4f1a\uff0c\u5b83\u7684\u5b9e\u8d28\u662f\u4e8c\u9879\u5f0f\u4e58\u6cd5\u7684\u9006\u8fc7\u7a0b\u3002\u5f53\u9996\u9879\u7cfb\u6570\u4e0d\u662f1\u65f6\uff0c\u5f80\u5f80\u9700\u8981\u591a\u6b21\u8bd5\u9a8c\uff0c\u52a1\u5fc5\u6ce8\u610f\u5404\u9879\u7cfb\u6570\u7684\u7b26\u53f7\u3002\u57fa\u672c\u5f0f\u5b50\uff1ax?+\uff08p+q\uff09x+pq=\uff08x+p\uff09\uff08x+q\uff09\u3002<\/p>\n
\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u53e3\u8bc0<\/p>\n
\u4e00\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u53e3\u8bc0\u662f\uff1a\u7ad6\u5206\u5e38\u6570\u4ea4\u53c9\u9a8c\uff0c\u6a2a\u5199\u56e0\u5f0f\u4e0d\u80fd\u4e71\u3002<\/p>\n
1\u3001\u53e3\u8bc0\u7b2c\u4e00\u53e5\uff1a\u7ad6\u5206\u5e38\u6570\u4ea4\u53c9\u9a8c\uff0c\u8fd9\u91cc\u5305\u542b\u4e86\u4e09\u4e2a\u6b65\u9aa4<\/p>\n
1\uff09\u7ad6\u5206\u4e8c\u6b21\u9879\u548c\u5e38\u6570\u9879\uff0c\u5373\u628a\u4e8c\u6b21\u9879\u548c\u5e38\u6570\u9879\u7684\u7cfb\u6570\u7ad6\u5411\u5199\u51fa\u6765\u3002<\/p>\n
2\uff09\u4ea4\u53c9\u76f8\u4e58\uff0c\u548c\u76f8\u52a0\uff0c\u5373\u659c\u5411\u76f8\u4e58\u7136\u540e\u76f8\u52a0\uff0c\u5f97\u51fa\u4e00\u6b21\u9879\u7cfb\u6570\u3002<\/p>\n
3\uff09\u68c0\u9a8c\u786e\u5b9a\uff0c\u68c0\u9a8c\u4e00\u6b21\u9879\u7cfb\u6570\u662f\u5426\u6b63\u786e\u3002<\/p>\n
2\u3001\u53e3\u8bc0\u7b2c\u4e8c\u53e5\uff1a\u6a2a\u5199\u56e0\u5f0f\u4e0d\u80fd\u4e71<\/p>\n
\u5373\u628a\u56e0\u5f0f\u6a2a\u5411\u5199\uff0c\u800c\u4e0d\u662f\u4ea4\u53c9\u5199\uff0c\u8fd9\u91cc\u4e0d\u80fd\u641e\u4e71\u3002<\/p>\n
\u4e8c\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u987a\u53e3\u6e9c\uff1a\u5206\u89e3\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u5c1d\u8bd5\u5341\u5b57\u76f8\u4e58\u6cd5\u3002<\/p>\n
\u5206\u89e3\u4e8c\u6b21\u5e38\u6570\u9879\uff0c\u4ea4\u53c9\u76f8\u4e58\u505a\u52a0\u6cd5\u3002<\/p>\n
\u53c9\u4e58\u548c\u662f\u4e00\u6b21\u9879\uff0c\u5341\u5b57\u76f8\u4e58\u5206\u89e3\u5b83\u3002<\/p>\n
\u5341\u5b57\u76f8\u4e58\u6cd5\u8c01\u63d0\u51fa\u7684<\/p>\n
\u5341\u5b57\u76f8\u4e58\u6cd5\u662f\u4e00\u79cd\u7528\u4e8e\u5206\u89e3\u4e8c\u6b21\u591a\u9879\u5f0f\u7684\u6570\u5b66\u65b9\u6cd5\uff0c\u5b83\u7684\u53d1\u660e\u8005\u662f\u610f\u5927\u5229\u6570\u5b66\u5bb6\u6bd5\u8fbe\u54e5\u62c9\u65af\u3002<\/p>\n
\u636e\u4f20\u8bf4\uff0c\u6bd5\u8fbe\u54e5\u62c9\u65af\u6709\u4e00\u6b21\u5728\u6c99\u6ee9\u4e0a\u6563\u6b65\u65f6\uff0c\u770b\u5230\u6709\u4e9b\u4eba\u7528\u5c0f\u77f3\u5b50\u5728\u6c99\u6ee9\u4e0a\u753b\u51fa\u4e86\u4e00\u4e2a\u4e09\u89d2\u5f62\u548c\u4e00\u4e2a\u6b63\u65b9\u5f62\uff0c\u5e76\u4e14\u5b83\u4eec\u6709\u516c\u5171\u8fb9\u3002\u4ed6\u7531\u6b64\u53d7\u5230\u542f\u53d1\uff0c\u5e76\u53d1\u73b0\u4e86\u5341\u5b57\u76f8\u4e58\u6cd5\u3002<\/p>\n
\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u5177\u4f53\u6b65\u9aa4\u662f\u5c06\u4e8c\u6b21\u9879\u548c\u5e38\u6570\u9879\u5206\u522b\u653e\u5728\u4e00\u4e2a\u5341\u5b57\u5f62\u7684\u4e24\u4e2a\u659c\u5bf9\u89d2\u4e0a\uff0c\u5c06\u4e00\u6b21\u9879\u653e\u5728\u5341\u5b57\u5f62\u7684\u4e2d\u5fc3\u7ebf\u4e0a\uff0c\u7136\u540e\u5c06\u56db\u4e2a\u6570\u76f8\u4e58\u3002\u5982\u679c\u4e58\u79ef\u7684\u4e24\u4e2a\u6570\u5b57\u76f8\u540c\uff0c\u5219\u8bf4\u660e\u8fd9\u4e2a\u4e8c\u6b21\u591a\u9879\u5f0f\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e24\u4e2a\u4e00\u6b21\u591a\u9879\u5f0f\u7684\u4e58\u79ef\uff1b\u5982\u679c\u4e58\u79ef\u7684\u4e24\u4e2a\u6570\u5b57\u4e92\u8d28\uff0c\u5219\u8bf4\u660e\u8fd9\u4e2a\u4e8c\u6b21\u591a\u9879\u5f0f\u4e0d\u80fd\u5206\u89e3\u4e3a\u4e24\u4e2a\u4e00\u6b21\u591a\u9879\u5f0f\u7684\u4e58\u79ef\u3002<\/p>\n
\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u53d1\u73b0\u5bf9\u6570\u5b66\u7684\u53d1\u5c55\u4ea7\u751f\u4e86\u6df1\u8fdc\u7684\u5f71\u54cd\uff0c\u5b83\u4f7f\u5f97\u5206\u89e3\u4e8c\u6b21\u591a\u9879\u5f0f\u53d8\u5f97\u66f4\u52a0\u7b80\u5355\u548c\u9ad8\u6548\u3002\u540c\u65f6\uff0c\u5b83\u4e5f\u4e3a\u540e\u6765\u7684\u6570\u5b66\u5bb6\u63d0\u4f9b\u4e86\u66f4\u591a\u7684\u5de5\u5177\u548c\u601d\u8def\u6765\u7814\u7a76\u4e8c\u6b21\u65b9\u7a0b\u548c\u4e8c\u6b21\u51fd\u6570\u3002<\/p>\n
\u7ec3\u4e60\u9898\uff1a<\/p>\n
1.x?-8x+15=0<\/p>\n
2.6x?-5x-25=0<\/p>\n
3.a?-7a+6=0<\/p>\n
4.8x?+6x-35=0<\/p>\n
5.18x?-21x+5=0<\/p>\n
6.20-9y-20y?=0<\/p>\n
7.2x?+3x+1=0<\/p>\n
8.2y?+y-6=0<\/p>\n
9.6x?-13x+6=0<\/p>\n
10.3a?-7a-6=0<\/p>\n
11.6x?-11x+3=0<\/p>\n
12.4m?+8m+3=0<\/p>\n
13.10x?-21x+2=0<\/p>\n
14.8m?-22m+15=0<\/p>\n
15.4n?+4n-15=0<\/p>\n
\u89e3\u9898\u601d\u8def\uff1a<\/p>\n
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