十字相乘法练习题 急求!! 给我点十字相乘法的题，谢了！要100道，最好有答案
\u5341\u5b57\u76f8\u4e58\u6cd5\u7ec3\u4e60\u9898\uff081\uff09q\u4e3a\u6b63\u6570\u65f6\uff0ca\u3001b \uff08 \u540c\u53f7 \uff09 \uff0c\u4e14\u4e0e \uff08 p\uff09 \u540c\u53f7\uff1b
\uff082\uff09q\u4e3a\u8d1f\u6570\u65f6\uff0ca\u3001b \uff08 \u5f02\u53f7 \uff09 \uff0c\u5176\u4e2d\u7edd\u5bf9\u503c \uff08\u201c\u8f83\u5927\u201d\uff09\uff08\u586b\u201c\u8f83\u5927\u201d\u6216\u201c\u8f83\u5c0f\u201d\uff09\u56e0\u6570\u4e0ep\u540c\u53f7\uff1b
\uff083\uff09\u5148\u628a\uff08q )\u5206\u89e3\u6210\u82e5\u5e72\u7ec4\u4e24\u6570\u4e4b\u79ef\uff0c\u9009\u62e9\u5176\u4e2d\u4e24\u6570\u4e4b\u548c\u7b49\u4e8e(p) \u7684\u4e00\u7ec4\u6570\u3002
\u5341\u5b57\u76f8\u4e58\u6cd5\u867d\u7136\u6bd4\u8f83\u96be\u5b66,\u4f46\u662f\u4e00\u65e6\u5b66\u4f1a\u4e86\u5b83,\u7528\u5b83\u6765\u89e3\u9898,\u4f1a\u7ed9\u6211\u4eec\u5e26\u6765\u5f88\u591a\u65b9\u4fbf,\u4ee5\u4e0b\u662f\u6211\u5bf9\u5341\u5b57\u76f8\u4e58\u6cd5\u63d0\u51fa\u7684\u4e00\u4e9b\u4e2a\u4eba\u89c1\u89e3\u3002
1\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u65b9\u6cd5\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
2\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u7528\u5904\uff1a\uff081\uff09\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u5206\u89e3\u56e0\u5f0f\u3002\uff082\uff09\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u3002
3\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u4f18\u70b9\uff1a\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u9898\u7684\u901f\u5ea6\u6bd4\u8f83\u5feb\uff0c\u80fd\u591f\u8282\u7ea6\u65f6\u95f4\uff0c\u800c\u4e14\u8fd0\u7528\u7b97\u91cf\u4e0d\u5927\uff0c\u4e0d\u5bb9\u6613\u51fa\u9519\u3002
4\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u7f3a\u9677\uff1a1\u3001\u6709\u4e9b\u9898\u76ee\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u6bd4\u8f83\u7b80\u5355\uff0c\u4f46\u5e76\u4e0d\u662f\u6bcf\u4e00\u9053\u9898\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u90fd\u7b80\u5355\u30022\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u53ea\u9002\u7528\u4e8e\u4e8c\u6b21\u4e09\u9879\u5f0f\u7c7b\u578b\u7684\u9898\u76ee\u30023\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u6bd4\u8f83\u96be\u5b66\u3002
5\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u9898\u5b9e\u4f8b\uff1a
1)\u3001 \u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u4e00\u4e9b\u7b80\u5355\u5e38\u89c1\u7684\u9898\u76ee
\u4f8b1\u628am²+4m-12\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u672c\u9898\u4e2d\u5e38\u6570\u9879-12\u53ef\u4ee5\u5206\u4e3a-1\u00d712\uff0c-2\u00d76\uff0c-3\u00d74\uff0c-4\u00d73\uff0c-6\u00d72\uff0c-12\u00d71\u5f53-12\u5206\u6210-2\u00d76\u65f6\uff0c\u624d\u7b26\u5408\u672c\u9898
\u89e3\uff1a\u56e0\u4e3a 1 -2
1 \u2573 6
\u6240\u4ee5m²+4m-12=\uff08m-2\uff09\uff08m+6\uff09
\u4f8b2\u628a5²+6x-8\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u672c\u9898\u4e2d\u76845\u53ef\u5206\u4e3a1\u00d75,-8\u53ef\u5206\u4e3a-1\u00d78\uff0c-2\u00d74\uff0c-4\u00d72\uff0c-8\u00d71\u3002\u5f53\u4e8c\u6b21\u9879\u7cfb\u6570\u5206\u4e3a1\u00d75\uff0c\u5e38\u6570\u9879\u5206\u4e3a-4\u00d72\u65f6\uff0c\u624d\u7b26\u5408\u672c\u9898
\u89e3\uff1a \u56e0\u4e3a 1 2
5 \u2573 -4
\u6240\u4ee55²+6x-8=\uff08x+2\uff09\uff085x-4\uff09
\u4f8b3\u89e3\u65b9\u7a0bx²-8x+15=0
\u5206\u6790\uff1a\u628ax²-8x+15\u770b\u6210\u5173\u4e8ex\u7684\u4e00\u4e2a\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u521915\u53ef\u5206\u62101\u00d715\uff0c3\u00d75\u3002
\u89e3\uff1a \u56e0\u4e3a 1 -3
1 \u2573 -5
\u6240\u4ee5\u539f\u65b9\u7a0b\u53ef\u53d8\u5f62\uff08x-3\uff09\uff08x-5\uff09=0
\u6240\u4ee5x1=3 x2=5
\u4f8b4\u3001\u89e3\u65b9\u7a0b 6²-5x-25=0
\u5206\u6790\uff1a\u628a6²5x-25\u770b\u6210\u4e00\u4e2a\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u52196\u53ef\u4ee5\u5206\u4e3a1\u00d76\uff0c2\u00d73\uff0c-25\u53ef\u4ee5\u5206\u6210-1\u00d725\uff0c-5\u00d75\uff0c-25\u00d71\u3002
\u89e3\uff1a \u56e0\u4e3a 2 -5
3 \u2573 5
\u6240\u4ee5 \u539f\u65b9\u7a0b\u53ef\u53d8\u5f62\u6210\uff082x-5\uff09\uff083x+5\uff09=0
\u6240\u4ee5 x1=5/2 x2=-5/3
2)\u3001\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u4e00\u4e9b\u6bd4\u8f83\u96be\u7684\u9898\u76ee
\u4f8b5\u628a14²-67xy+18y²\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u628a14x²-67xy+18y²\u770b\u6210\u662f\u4e00\u4e2a\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f,\u521914\u53ef\u5206\u4e3a1\u00d714,2\u00d77, 18y²\u53ef\u5206\u4e3ay.18y , 2y.9y , 3y.6y
\u89e3: \u56e0\u4e3a 2 -9y
7 \u2573 -2y
\u6240\u4ee5 14x²-67xy+18y²= (2x-2y)(7x-9y)
\u4f8b6 \u628a10x²-27xy-28y²-x+25y-3\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u5728\u672c\u9898\u4e2d\uff0c\u8981\u628a\u8fd9\u4e2a\u591a\u9879\u5f0f\u6574\u7406\u6210\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u5f62\u5f0f
\u89e3\u6cd5\u4e00\u300110x²-27xy-28y²-x+25y-3
=10x²-\uff0827y+1\uff09x -\uff0828y²;-25y+3\uff09
4y -3
7y \u2573 -1
=10x²-\uff0827y+1\uff09x -\uff084y-3\uff09\uff087y -1\uff09
=[2x -\uff087y -1\uff09][5x +\uff084y -3\uff09] 2 -\uff087y \u2013 1\uff09
5 \u2573 4y - 3
=\uff082x -7y +1\uff09\uff085x +4y -3\uff09
\u8bf4\u660e\uff1a\u5728\u672c\u9898\u4e2d\u5148\u628a28y²-25y+3\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a\uff084y-3\uff09\uff087y -1\uff09\uff0c\u518d\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a10x²-\uff0827y+1\uff09x -\uff084y-3\uff09\uff087y -1\uff09\u5206\u89e3\u4e3a[2x -\uff087y -1\uff09][5x +\uff084y+3\uff09]
\u89e3\u6cd5\u4e8c\u300110x²-27xy-28y²-x+25y-3
=\uff082x -7y\uff09\uff085x +4y\uff09-\uff08x -25y\uff09- 3 2 -7y
=[\uff082x -7y\uff09+1] [\uff085x -4y\uff09-3] 5 \u2573 4y
=\uff082x -7y+1\uff09\uff085x -4y -3\uff09 2 x -7y 1
5 x - 4y \u2573 -3
\u8bf4\u660e:\u5728\u672c\u9898\u4e2d\u5148\u628a10x²-27xy-28y²\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a\uff082x -7y\uff09\uff085x +4y\uff09,\u518d\u628a\uff082x -7y\uff09\uff085x +4y\uff09-\uff08x -25y\uff09- 3\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a[\uff082x -7y\uff09+1] [\uff085x -4y\uff09-3].
\u4f8b7\uff1a\u89e3\u5173\u4e8ex\u65b9\u7a0b\uff1ax²- 3ax + 2a²\u2013ab -b²=0
\u5206\u6790\uff1a2a²\u2013ab-b²\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3
\u89e3\uff1ax²- 3ax + 2a²\u2013ab -b²=0
x²- 3ax +\uff082a²\u2013ab - b²\uff09=0
x²- 3ax +\uff082a+b\uff09\uff08a-b\uff09=0 1 -b
2 \u2573 +b
[x-\uff082a+b\uff09][ x-\uff08a-b\uff09]=0 1 -\uff082a+b\uff09
1 \u2573 -\uff08a-b\uff09
\u6240\u4ee5 x1=2a+b x2=a-b
\u6ce8\u610f
1.\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a\u67d0\u4e9b\u5f62\u5982ax2+bx+c\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u5e94\u6ce8\u610f\u4ee5\u4e0b\u95ee\u9898\uff1a
(1)\u6b63\u786e\u7684\u5341\u5b57\u76f8\u4e58\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a
a1 c1
\u5728\u5f0f\u5b50 � \u4e2d\uff0c\u7ad6\u5411\u7684\u4e24\u4e2a\u6570\u5fc5\u987b\u6ee1\u8db3\u5173\u7cfba1a2=a\uff0cc1c2=c\uff1b\u5728\u4e0a\u5f0f\u4e2d\uff0c\u659c\u5411\u7684
a2 c2
\u4e24\u4e2a\u6570\u5fc5\u987b\u6ee1\u8db3\u5173\u7cfba1c2+a2c1=b.
(2)\u7531\u5341\u5b57\u76f8\u4e58\u7684\u56fe\u4e2d\u7684\u56db\u4e2a\u6570\u5199\u51fa\u5206\u89e3\u540e\u7684\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u65f6\uff0c\u56fe\u7684\u4e0a\u4e00\u884c\u4e24\u4e2a\u6570\u4e2d\uff0ca1\u662f\u7b2c\u4e00\u4e2a\u56e0\u5f0f\u4e2d\u7684\u4e00\u6b21\u9879\u7cfb\u6570\uff0cc1\u662f\u5e38\u6570\u9879\uff1b\u5728\u4e0b\u4e00\u884c\u7684\u4e24\u4e2a\u6570\u4e2d\uff0ca2\u662f\u7b2c\u4e8c\u4e2a\u56e0\u5f0f\u4e2d\u7684\u4e00\u6b21\u9879\u7684\u7cfb\u6570\uff0cc2\u662f\u5e38\u6570\u9879.
(3)\u4e8c\u6b21\u9879\u7cfb\u6570a\u4e00\u822c\u90fd\u628a\u5b83\u770b\u4f5c\u662f\u6b63\u6570(\u5982\u679c\u662f\u8d1f\u6570\uff0c\u5219\u5e94\u63d0\u51fa\u8d1f\u53f7\uff0c\u5229\u7528\u6052\u7b49\u53d8\u5f62\u628a\u5b83\u8f6c\u5316\u4e3a\u6b63\u6570\uff0c)\u53ea\u9700\u628a\u5b83\u5206\u89e3\u6210\u4e24\u4e2a\u6b63\u7684\u56e0\u6570.
2.\u5f62\u5982x+px+q\u7684\u67d0\u4e9b\u4e8c\u6b21\u4e09\u9879\u5f0f\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f.
3.\u51e1\u662f\u53ef\u7528\u4ee3\u6362\u7684\u65b9\u6cd5\u8f6c\u5316\u4e3a\u4e8c\u6b21\u4e09\u9879\u5f0fax+bx+c\u7684\u591a\u9879\u5f0f\uff0c\u6709\u4e9b\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff0c\u5982\u4f8b4.
x²+6x+8=(x+2)(x+4)
x²-7x+10=(x-2)(x-5)
x²-3x-10=(x+2)(x-5)
x²+8x-20=(x-2)(x+10)
2x²+5x-3=(2x-1)(x+3)
6x²-x-1=(2x-1)(3x+1)
3x²+5x-2=(x+2)(3x-1)
2x²+3x+1=(x+1)(2x+1)
4x²-17x+4=(x-4)(4x-1)
