需要先提公因数再十字相乘的因式分解练习题
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\u5206\u6790\uff1a\u6309\u7167\u4f8b1\u7684\u65b9\u6cd5\uff0c\u5206\u89e3\u4e8c\u6b21\u9879\u7cfb\u65706\u53ca\u5e38\u6570\u9879\uff0d5\uff0c\u628a\u5b83\u4eec\u5206\u522b\u6392\u5217\uff0c\u53ef\u67098\u79cd\u4e0d\u540c\u7684\u6392\u5217\u65b9\u6cd5\uff0c\u5176\u4e2d\u7684\u4e00\u79cd 2 1 3 \uff0d5 2\u00d7(\uff0d5)+3\u00d71=\uff0d7 \u662f\u6b63\u786e\u7684\uff0c\u56e0\u6b64\u539f\u591a\u9879\u5f0f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f. \u89e3 6x2\uff0d7x\uff0d5=(2x+1)(3x\uff0d5). \u6307\u51fa\uff1a\u901a\u8fc7\u4f8b1\u548c\u4f8b2\u53ef\u4ee5\u770b\u5230\uff0c\u8fd0\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a\u4e00\u4e2a\u4e8c\u6b21\u9879\u7cfb\u6570\u4e0d\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\uff0c\u5f80\u5f80\u8981\u7ecf\u8fc7\u591a\u6b21\u89c2\u5bdf\uff0c\u624d\u80fd\u786e\u5b9a\u662f\u5426\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f. \u5bf9\u4e8e\u4e8c\u6b21\u9879\u7cfb\u6570\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff0c\u8fd9\u65f6\u53ea\u9700\u8003\u8651\u5982\u4f55\u628a\u5e38\u6570\u9879\u5206\u89e3\u56e0\u6570.\u4f8b\u5982\u628ax2+2x\uff0d15\u5206\u89e3\u56e0\u5f0f\uff0c\u5341\u5b57\u76f8\u4e58\u6cd5\u662f 1 \uff0d3 1 5 1\u00d75+1\u00d7(\uff0d3)=2 \u6240\u4ee5x2+2x-15=(x\uff0d3)(x+5). \u4f8b3 \u628a5x2+6xy\uff0d8y2\u5206\u89e3\u56e0\u5f0f. \u5206\u6790\uff1a\u8fd9\u4e2a\u591a\u9879\u5f0f\u53ef\u4ee5\u770b\u4f5c\u662f\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u628a\uff0d8y2\u770b\u4f5c\u5e38\u6570\u9879\uff0c\u5728\u5206\u89e3\u4e8c\u6b21\u9879\u53ca\u5e38\u6570\u9879\u7cfb\u6570\u65f6\uff0c\u53ea\u9700\u5206\u89e35\u4e0e\uff0d8\uff0c\u7528\u5341\u5b57\u4ea4\u53c9\u7ebf\u5206\u89e3\u540e\uff0c\u7ecf\u8fc7\u89c2\u5bdf\uff0c\u9009\u53d6\u5408\u9002\u7684\u4e00\u7ec4\uff0c\u5373 1 2 5 \uff0d4 1\u00d7(\uff0d4)+5\u00d72=6 \u89e3 5x2+6xy\uff0d8y2=(x+2y)(5x\uff0d4y). \u6307\u51fa\uff1a\u539f\u5f0f\u5206\u89e3\u4e3a\u4e24\u4e2a\u5173\u4e8ex\uff0cy\u7684\u4e00\u6b21\u5f0f. \u4f8b4 \u628a(x\uff0dy)(2x\uff0d2y\uff0d3)\uff0d2\u5206\u89e3\u56e0\u5f0f. \u5206\u6790\uff1a\u8fd9\u4e2a\u591a\u9879\u5f0f\u662f\u4e24\u4e2a\u56e0\u5f0f\u4e4b\u79ef\u4e0e\u53e6\u4e00\u4e2a\u56e0\u6570\u4e4b\u5dee\u7684\u5f62\u5f0f\uff0c\u53ea\u6709\u5148\u8fdb\u884c\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\u8fd0\u7b97\uff0c\u628a\u53d8\u5f62\u540e\u7684\u591a\u9879\u5f0f\u518d\u56e0\u5f0f\u5206\u89e3. \u95ee\uff1a\u4e24\u4e0a\u4e58\u79ef\u7684\u56e0\u5f0f\u662f\u4ec0\u4e48\u7279\u70b9\uff0c\u7528\u4ec0\u4e48\u65b9\u6cd5\u8fdb\u884c\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\u8fd0\u7b97\u6700\u7b80\u4fbf? \u7b54\uff1a\u7b2c\u4e8c\u4e2a\u56e0\u5f0f\u4e2d\u7684\u524d\u4e24\u9879\u5982\u679c\u63d0\u51fa\u516c\u56e0\u5f0f2\uff0c\u5c31\u53d8\u4e3a2(x\uff0dy)\uff0c\u5b83\u662f\u7b2c\u4e00\u4e2a\u56e0\u5f0f\u7684\u4e8c\u500d\uff0c\u7136\u540e\u628a(x\uff0dy)\u770b\u4f5c\u4e00\u4e2a\u6574\u4f53\u8fdb\u884c\u4e58\u6cd5\u8fd0\u7b97\uff0c\u53ef\u628a\u539f\u591a\u9879\u5f0f\u53d8\u5f62\u4e3a\u5173\u4e8e(x\uff0dy)\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u5c31\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\u4e86. \u89e3 (x\uff0dy)(2x\uff0d2y\uff0d3)\uff0d2 =(x\uff0dy)[2(x\uff0dy)\uff0d3]\uff0d2 =2(x\uff0dy) 2\uff0d3(x\uff0dy)\uff0d2 =[(x\uff0dy)\uff0d2][2(x\uff0dy)+1] =(x\uff0dy\uff0d2)(2x\uff0d2y+1). 1 \uff0d2 2 +1 1\u00d71+2\u00d7(\uff0d2)=\uff0d3 \u6307\u51fa\uff1a\u628a(x\uff0dy)\u770b\u4f5c\u4e00\u4e2a\u6574\u4f53\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u8fd9\u53c8\u662f\u8fd0\u7528\u4e86\u6570\u5b66\u4e2d\u7684\u201c\u6574\u4f53\u201d\u601d\u60f3\u65b9\u6cd5. \u4e09\u3001\u8bfe\u5802\u7ec3\u4e60 1.\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff1a (1)2x2\uff0d5x\uff0d12\uff1b (2)3x2\uff0d5x\uff0d2\uff1b (3)6x2\uff0d13x+5\uff1b (4)7x2\uff0d19x\uff0d6\uff1b (5)12x2\uff0d13x+3\uff1b (6)4x2+24x+27. 2.\u628a\u4e0b\u5217\u5404\u5f0f\u5206\u89e3\u56e0\u5f0f\uff1a (1)6x2\uff0d13xy+6y2\uff1b (2)8x2y2+6xy\uff0d35\uff1b (3)18x2\uff0d21xy+5y2\uff1b (4)2(a+b) 2+(a+b)(a\uff0db)\uff0d6(a\uff0db) 2. \u7b54\u6848\uff1a 1.(1)(x\uff0d4)(2x+3)\uff1b (2)(x\uff0d2)(3x+1)\uff1b (3)(2x\uff0d1)(3x\uff0d5)\uff1b (4)(x\uff0d3)(7x+2)\uff1b (5)(3x\uff0d1)(4x\uff0d3)\uff1b (6)(2x+3)(2x+9). 2.(1)(2x\uff0d3y)(3x\uff0d2y)\uff1b (2)(2xy+5)(4xy\uff0d7)\uff1b (3)(3x\uff0dy)(6x\uff0d5y)\uff1b (4)(3a\uff0db)(5b\uff0da). \u56db\u3001\u5c0f\u7ed3 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\u5982x2+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\u5f0fax2+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. \u4e94\u3001\u4f5c\u4e1a 1.\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff1a (1)2x2+3x+1\uff1b (2)2y2+y\uff0d6\uff1b (3)6x2\uff0d13x+6\uff1b (4)3a2\uff0d7a\uff0d6\uff1b (5)6x2\uff0d11xy+3y2\uff1b (6)4m2+8mn+3n2\uff1b (7)10x2\uff0d21xy+2y2\uff1b (8)8m2\uff0d22mn+15n2. 2\uff0e\u628a\u4e0b\u5217\u5404\u5f0f\u5206\u89e3\u56e0\u5f0f\uff1a (1)4n2+4n\uff0d15\uff1b (2)6a2+a\uff0d35\uff1b (3)5x2\uff0d8x\uff0d13\uff1b (4)4x2+15x+9 (5)15x2+x\uff0d2\uff1b (6)6y2+19y+10\uff1b (7)20\uff0d9y\uff0d20y2\uff1b (8)7(x\uff0d1) 2+4(x\uff0d1)(y+2)\uff0d20(y+2) 2. \u7b54\u6848\uff1a 1.(1)(2x+1)(x+1)\uff1b (2)(y+2)(2y\uff0d3)\uff1b (3)(2x\uff0d3)(3x\uff0d2); (4)(a\uff0d3)(3a+2); (5)(2x\uff0d3y)(3x\uff0dy); (6)(2m+n)(2m+3n); (7)(x\uff0d2y)(10x\uff0dy); (8)(2m\uff0d3n)(4m\uff0d5n). 2.(1)(2n\uff0d3)(2n+5); (2)(2a+5)(3a\uff0d7); (3)(x+1)(5x-13); (4)(x+3)(4x+3); (5)(3x\uff0d1)(5x+2); (6)(2y+5)(3y+2); (7)\uff0d(4y+5)(5y\uff0d4); (8)(x+2y+3)(7x\uff0d10y\uff0d27).\u53c2\u8003\u8d44\u6599\uff1a http://www.cbe21.com/subject/maths/printer.php?article_id=269xue
★ 15x^2+25x+20
★ x^4-2x^2+1
★★ x^4+x^2+1
★ x^3+6x^2+7x
★★ (2a-b)^2+(b-2a)-6
★★★ x^2+2y^2+3z^2+3xy+4xz+5yz
★★ x^8+x^4+1
★★★ x^3-6x^2+11x-6
★★★★ 1+a+b+c+ab+ac+bc+abc
★★★★★ ba^3-ab^3+2a^2+2b^2+4
★★★★ xa^2+ax^2-abx+x^2-b^2+ax-cx+ab+bc-ca
★★★★ x^4-14x^3+61x^2-84x
6x2-12x-18
x³+2x²-3x=x(x+3)(x-1)
绛旓細鈽 15x^2+25x+20 鈽 x^4-2x^2+1 鈽呪槄 x^4+x^2+1 鈽 x^3+6x^2+7x 鈽呪槄 (2a-b)^2+(b-2a)-6 鈽呪槄鈽 x^2+2y^2+3z^2+3xy+4xz+5yz 鈽呪槄 x^8+x^4+1 鈽呪槄鈽 x^3-6x^2+11x-6 鈽呪槄鈽 1+a+b+c+ab+ac+bc+abc 鈽呪槄鈽 ba^3...
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