初一的因式分解怎么做，详细点 初一的因式分解怎么解
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1\u3001\u63d0\u53d6\u516c\u56e0\u5f0f\u6cd5\uff0c\u628a\u5404\u9879\u4e2d\u7684\u516c\u56e0\u5f0f\u6216\u516c\u56e0\u6570\u63d0\u53d6\uff0c\u7279\u522b\u4e0d\u8ba9\u4eba\u6ce8\u610f\u7684\u56e0\u6570\u5f80\u5f80\u88ab
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2\u3001\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\uff1a\u9879\u6570\u2014\u2014\u4e09\u9879\uff0c
\u6ee1\u8db3\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u2014\u2014(a\u00b1b)^2=a^2\u00b12ab+b^2\u3002
3\u3001\u5e73\u65b9\u5dee\u516c\u5f0f\uff1a\u9879\u6570\u2014\u2014\u4e24\u9879\uff0c
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4\u3001\u4efb\u4f55\u4e00\u4e2a\u56e0\u5f0f\u5206\u89e3\u9898\u5148\u770b\u662f\u5426\u6709\u516c\u56e0\u5f0f(\u6570)\u53ef\u63d0\u53d6\uff0c
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1.\u5206\u89e3\u56e0\u5f0f(1+y)-2x(1+y)+x(1-y) \u89e3\uff1a\u539f\u5f0f=(1+y)+2(1+y)+x(1-y)+x(1-y)-2(1+y)x(1-y)-2x(1+y) =[(1+y)+x(1-y)]-2(1+y)x(1-y)-2x(1+y) =[(1+y)+x(1-y)]-(2x) =[(1+y)+x(1-y)+2x]\u00b7[(1+y)+x(1-y)-2x] =(x-xy+2x+y+1)(x-xy-2x+y+1) =[(x+1)-y(x-1)][(x-1)-y(x-1)] =(x+1)(x+1-xy+y)(x-1)(x-1-xy-y) 2.\u8bc1\u660e\uff1a\u5bf9\u4e8e\u4efb\u4f55\u6570x,y\uff0c\u4e0b\u5f0f\u7684\u503c\u90fd\u4e0d\u4f1a\u4e3a33 x^5+3x^4y-5x^3y^2+4xy^4+12y^5 \u89e3\uff1a\u539f\u5f0f=(x^5+3x^4y)-(5x^3y^2+15x^2y^3)+(4xy^4+12y^5) =x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y) =(x+3y)(x^4-5x^2y^2+4y^4) =(x+3y)(x^2-4y^2)(x^2-y^2) =(x+3y)(x+y)(x-y)(x+2y)(x-2y) \u5c31\u662f\u628a\u7b80\u5355\u7684\u95ee\u9898\u590d\u6742\u5316\uff09 \u6ce8\u610f\u4e09\u539f\u5219 1 \u5206\u89e3\u8981\u5f7b\u5e95 2 \u6700\u540e\u7ed3\u679c\u53ea\u6709\u5c0f\u62ec\u53f7 3 \u6700\u540e\u7ed3\u679c\u4e2d\u591a\u9879\u5f0f\u9996\u9879\u7cfb\u6570\u4e3a\u6b63\uff08\u4f8b\u5982\uff1a-3x^2+x=x(-3x+1\uff09\uff09 \u5f52\u7eb3\u65b9\u6cd5\uff1a\u5317\u5e08\u5927\u7248\u516b\u4e0b\u8bfe\u672c\u4e0a\u6709\u7684 1\u3001\u63d0\u516c\u56e0\u5f0f\u6cd5\u3002 2\u3001\u516c\u5f0f\u6cd5\u3002 3\u3001\u5206\u7ec4\u5206\u89e3\u6cd5\u3002 4\u3001\u51d1\u6570\u6cd5\u3002[x^2+(a+b)x+ab=(x+a)(x+b)] 5\u3001\u7ec4\u5408\u5206\u89e3\u6cd5\u3002 6\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u3002 7\u3001\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u3002 8\u3001\u914d\u65b9\u6cd5\u3002 9\u3001\u62c6\u9879\u6cd5\u3002 10\u3001\u6362\u5143\u6cd5\u3002 11\u3001\u957f\u9664\u6cd5\u3002 12\u3001\u52a0\u51cf\u9879\u6cd5\u3002 13\u3001\u6c42\u6839\u6cd5\u3002 14\u3001\u56fe\u8c61\u6cd5\u3002 15\u3001\u4e3b\u5143\u6cd5\u3002 16\u3001\u5f85\u5b9a\u7cfb\u6570\u6cd5\u3002 17\u3001\u7279\u6b8a\u503c\u6cd5\u3002 18\u3001\u56e0\u5f0f\u5b9a\u7406\u6cd5\u3002
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\u5982\u679c\u628a\u4e58\u6cd5\u516c\u5f0f\u53cd\u8fc7\u6765\uff0c\u5c31\u53ef\u4ee5\u628a\u67d0\u4e9b\u591a\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53eb\u516c\u5f0f\u6cd5\u3002 \u5e73\u65b9\u5dee\u516c\u5f0f: (a+b)(a-b)=a^2-b^2 \u53cd\u8fc7\u6765\u4e3aa^2-b^2=(a+b)(a-b) \u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\uff1a(a+b)^2=a^2+2ab+b^2 \u53cd\u8fc7\u6765\u4e3aa^2+2ab+b^2=(a+b)^2 (a-b)^2=a^2-2ab+b^2 a^2-2ab+b^2=(a-b)^2 \u6ce8\u610f\uff1a\u80fd\u8fd0\u7528\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u5206\u89e3\u56e0\u5f0f\u7684\u591a\u9879\u5f0f\u5fc5\u987b\u662f\u4e09\u9879\u5f0f\uff0c\u5176\u4e2d\u6709\u4e24\u9879\u80fd\u5199\u6210\u4e24\u4e2a\u6570(\u6216\u5f0f)\u7684\u5e73\u65b9\u548c\u7684\u5f62\u5f0f\uff0c\u53e6\u4e00\u9879\u662f\u8fd9\u4e24\u4e2a\u6570(\u6216\u5f0f)\u7684\u79ef\u76842\u500d\u3002 \u4e24\u6839\u5f0f\uff1aax^2+bx+c=a(x-(-b+\u221a(b^2-4ac))/2a)(x-(-b-\u221a(b^2-4ac))/2a) \u7acb\u65b9\u548c\u516c\u5f0f\uff1aa^3+b^3=(a+b)(a^2-ab+b^2)\uff1b \u7acb\u65b9\u5dee\u516c\u5f0f\uff1aa^3-b^3=(a-b)(a^2+ab+b^2)\uff1b \u5b8c\u5168\u7acb\u65b9\u516c\u5f0f\uff1aa^3\u00b13a^2b\uff0b3ab^2\u00b1b^3=(a\u00b1b)^3\uff0e \u516c\u5f0f\uff1aa^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca) \u4f8b\u5982\uff1aa^2+4ab+4b^2 =(a+2b)^2\u3002
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1\u3002 2.\u5206\u89e3\u56e0\u5f0f\u6280\u5de7\u638c\u63e1\uff1a \u2460\u7b49\u5f0f\u5de6\u8fb9\u5fc5\u987b\u662f\u591a\u9879\u5f0f\uff1b \u2461\u5206\u89e3\u56e0\u5f0f\u7684\u7ed3\u679c\u5fc5\u987b\u662f\u4ee5\u4e58\u79ef\u7684\u5f62\u5f0f\u8868\u793a\uff1b \u2462\u6bcf\u4e2a\u56e0\u5f0f\u5fc5\u987b\u662f\u6574\u5f0f\uff0c\u4e14\u6bcf\u4e2a\u56e0\u5f0f\u7684\u6b21\u6570\u90fd\u5fc5\u987b\u4f4e\u4e8e\u539f\u6765\u591a\u9879\u5f0f\u7684\u6b21\u6570\uff1b \u2463\u5206\u89e3\u56e0\u5f0f\u5fc5\u987b\u5206\u89e3\u5230\u6bcf\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u4e3a\u6b62\u3002 \u6ce8\uff1a\u5206\u89e3\u56e0\u5f0f\u524d\u5148\u8981\u627e\u5230\u516c\u56e0\u5f0f\uff0c\u5728\u786e\u5b9a\u516c\u56e0\u5f0f\u524d\uff0c\u5e94\u4ece\u7cfb\u6570\u548c\u56e0\u5f0f\u4e24\u4e2a\u65b9\u9762\u8003\u8651\u3002 3.\u63d0\u516c\u56e0\u5f0f\u6cd5\u57fa\u672c\u6b65\u9aa4\uff1a \uff081\uff09\u627e\u51fa\u516c\u56e0\u5f0f\uff1b \uff082\uff09\u63d0\u516c\u56e0\u5f0f\u5e76\u786e\u5b9a\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff1a \u2460\u7b2c\u4e00\u6b65\u627e\u516c\u56e0\u5f0f\u53ef\u6309\u7167\u786e\u5b9a\u516c\u56e0\u5f0f\u7684\u65b9\u6cd5\u5148\u786e\u5b9a\u7cfb\u6570\u518d\u786e\u5b9a\u5b57\u6bcd\uff1b \u2461\u7b2c\u4e8c\u6b65\u63d0\u516c\u56e0\u5f0f\u5e76\u786e\u5b9a\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff0c\u6ce8\u610f\u8981\u786e\u5b9a\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff0c\u53ef\u7528\u539f\u591a\u9879\u5f0f\u9664\u4ee5\u516c\u56e0\u5f0f\uff0c\u6240\u5f97\u7684\u5546\u5373\u662f\u63d0\u516c\u56e0\u5f0f\u540e\u5269\u4e0b\u7684\u4e00\u4e2a\u56e0\u5f0f\uff0c\u4e5f\u53ef\u7528\u516c\u56e0\u5f0f\u5206\u522b\u9664\u53bb\u539f\u591a\u9879\u5f0f\u7684\u6bcf\u4e00\u9879\uff0c\u6c42\u7684\u5269\u4e0b\u7684\u53e6\u4e00\u4e2a\u56e0\u5f0f\uff1b \u2462\u63d0\u5b8c\u516c\u56e0\u5f0f\u540e\uff0c\u53e6\u4e00\u56e0\u5f0f\u7684\u9879\u6570\u4e0e\u539f\u591a\u9879\u5f0f\u7684\u9879\u6570\u76f8\u540c\u3002
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\u5206\u7ec4\u5206\u89e3\u662f\u89e3\u65b9\u7a0b\u7684\u4e00\u79cd\u7b80\u6d01\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u6765\u5b66\u4e60\u8fd9\u4e2a\u77e5\u8bc6\u3002 \u80fd\u5206\u7ec4\u5206\u89e3\u7684\u65b9\u7a0b\u6709\u56db\u9879\u6216\u5927\u4e8e\u56db\u9879\uff0c\u4e00\u822c\u7684\u5206\u7ec4\u5206\u89e3\u6709\u4e24\u79cd\u5f62\u5f0f\uff1a\u4e8c\u4e8c\u5206\u6cd5\uff0c\u4e09\u4e00\u5206\u6cd5\u3002 \u6bd4\u5982\uff1a ax+ay+bx+by =a(x+y)+b(x+y) =(a+b)(x+y) \u6211\u4eec\u628aax\u548cay\u5206\u4e00\u7ec4\uff0cbx\u548cby\u5206\u4e00\u7ec4\uff0c\u5229\u7528\u4e58\u6cd5\u5206\u914d\u5f8b\uff0c\u4e24\u4e24\u76f8\u914d\uff0c\u7acb\u5373\u89e3\u9664\u4e86\u56f0\u96be\u3002 \u540c\u6837\uff0c\u8fd9\u9053\u9898\u4e5f\u53ef\u4ee5\u8fd9\u6837\u505a\u3002 ax+ay+bx+by =x(a+b)+y(a+b) =(a+b)(x+y) \u51e0\u9053\u4f8b\u9898\uff1a 1. 5ax+5bx+3ay+3by \u89e3\u6cd5\uff1a=5x(a+b)+3y(a+b) =(5x+3y)(a+b) \u8bf4\u660e\uff1a\u7cfb\u6570\u4e0d\u4e00\u6837\u4e00\u6837\u53ef\u4ee5\u505a\u5206\u7ec4\u5206\u89e3\uff0c\u548c\u4e0a\u9762\u4e00\u6837\uff0c\u628a5ax\u548c5bx\u770b\u6210\u6574\u4f53\uff0c\u628a3ay\u548c3by\u770b\u6210\u4e00\u4e2a\u6574\u4f53\uff0c\u5229\u7528\u4e58\u6cd5\u5206\u914d\u5f8b\u8f7b\u677e\u89e3\u51fa\u3002 2. x^3-x^2+x-1 \u89e3\u6cd5\uff1a=(x^3-x^2)+(x-1) =x^2(x-1)+ (x-1) =(x-1)(x^2+1) \u5229\u7528\u4e8c\u4e8c\u5206\u6cd5\uff0c\u63d0\u516c\u56e0\u5f0f\u6cd5\u63d0\u51fa x2\uff0c\u7136\u540e\u76f8\u5408\u8f7b\u677e\u89e3\u51b3\u3002 3. x^2-x-y^2-y \u89e3\u6cd5\uff1a=(x^2-y^2)-(x+y) =(x+y)(x-y)-(x+y) =(x+y)(x-y-1) \u5229\u7528\u4e8c\u4e8c\u5206\u6cd5\uff0c\u518d\u5229\u7528\u516c\u5f0f\u6cd5a^2-b^2=(a+b)(a-b)\uff0c\u7136\u540e\u76f8\u5408\u89e3\u51b3\u3002
\u5341\u5b57\u76f8\u4e58\u6cd5
\u8fd9\u79cd\u65b9\u6cd5\u6709\u4e24\u79cd\u60c5\u51b5\u3002 \u2460x^2+(p+q)x+pq\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3 \u8fd9\u7c7b\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u7279\u70b9\u662f\uff1a\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\uff1b\u5e38\u6570\u9879\u662f\u4e24\u4e2a\u6570\u7684\u79ef\uff1b\u4e00\u6b21\u9879\u7cfb\u6570\u662f\u5e38\u6570\u9879\u7684\u4e24\u4e2a\u56e0\u6570\u7684\u548c\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u76f4\u63a5\u5c06\u67d0\u4e9b\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\uff1ax^2+(p+q)x+pq=(x+p)(x+q) \uff0e \u2461kx^2+mx+n\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3 \u5982\u679c\u6709k=ad\uff0cn=cb\uff0c\u4e14\u6709ad+bc=m\u65f6\uff0c\u90a3\u4e48kx^2+mx+n=(ax+c)(dx+b)\uff0e \u56fe\u793a\u5982\u4e0b\uff1a a\u2572\u2571c b\u2571\u2572d \u4f8b\u5982\uff1a\u56e0\u4e3a 1 \u2572\u25712 -3\u2571\u2572 7 -3\u00d77=-21\uff0c1\u00d72=2\uff0c\u4e142-21=-19\uff0c \u6240\u4ee57x2-19x-6=(7x+2)(x-3)\uff0e \u5341\u5b57\u76f8\u4e58\u6cd5\u53e3\u8bc0\uff1a\u9996\u5c3e\u5206\u89e3\uff0c\u4ea4\u53c9\u76f8\u4e58\uff0c\u6c42\u548c\u51d1\u4e2d
\u62c6\u9879\u3001\u6dfb\u9879\u6cd5
\u8fd9\u79cd\u65b9\u6cd5\u6307\u628a\u591a\u9879\u5f0f\u7684\u67d0\u4e00\u9879\u62c6\u5f00\u6216\u586b\u8865\u4e0a\u4e92\u4e3a\u76f8\u53cd\u6570\u7684\u4e24\u9879\uff08\u6216\u51e0\u9879\uff09\uff0c\u4f7f\u539f\u5f0f\u9002\u5408\u4e8e\u63d0\u516c\u56e0\u5f0f\u6cd5\u3001\u8fd0\u7528\u516c\u5f0f\u6cd5\u6216\u5206\u7ec4\u5206\u89e3\u6cd5\u8fdb\u884c\u5206\u89e3\u3002\u8981\u6ce8\u610f\uff0c\u5fc5\u987b\u5728\u4e0e\u539f\u591a\u9879\u5f0f\u76f8\u7b49\u7684\u539f\u5219\u4e0b\u8fdb\u884c\u53d8\u5f62\u3002 \u4f8b\u5982\uff1abc(b+c)+ca(c-a)-ab(a+b) =bc(c-a+a+b)+ca(c-a)-ab(a+b) =bc(c-a)+bc(a+b)+ca(c-a)-ab(a+b) =bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b) =(bc+ca)(c-a)+(bc-ab)(a+b) =c(c-a)(b+a)+b(a+b)(c-a) =(c+b)(c-a)(a+b)\uff0e
\u914d\u65b9\u6cd5
\u5bf9\u4e8e\u67d0\u4e9b\u4e0d\u80fd\u5229\u7528\u516c\u5f0f\u6cd5\u7684\u591a\u9879\u5f0f\uff0c\u53ef\u4ee5\u5c06\u5176\u914d\u6210\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u7136\u540e\u518d\u5229\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\uff0c\u5c31\u80fd\u5c06\u5176\u56e0\u5f0f\u5206\u89e3\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53eb\u914d\u65b9\u6cd5\u3002\u5c5e\u4e8e\u62c6\u9879\u3001\u8865\u9879\u6cd5\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\u3002\u4e5f\u8981\u6ce8\u610f\u5fc5\u987b\u5728\u4e0e\u539f\u591a\u9879\u5f0f\u76f8\u7b49\u7684\u539f\u5219\u4e0b\u8fdb\u884c\u53d8\u5f62\u3002 \u4f8b\u5982\uff1ax^2+3x-40 =x^2+3x+2.25-42.25 =(x+1.5)^2-(6.5)^2 =(x+8)(x-5)\uff0e
\u5e94\u7528\u56e0\u5f0f\u5b9a\u7406
\u5bf9\u4e8e\u591a\u9879\u5f0ff(x)=0\uff0c\u5982\u679cf(a)=0\uff0c\u90a3\u4e48f(x)\u5fc5\u542b\u6709\u56e0\u5f0fx-a\uff0e \u4f8b\u5982\uff1af(x)=x^2+5x+6\uff0cf(-2)=0\uff0c\u5219\u53ef\u786e\u5b9ax+2\u662fx^2+5x+6\u7684\u4e00\u4e2a\u56e0\u5f0f\u3002(\u4e8b\u5b9e\u4e0a\uff0cx^2+5x+6=(x+2)(x+3)\uff0e) \u6ce8\u610f\uff1a1\u3001\u5bf9\u4e8e\u7cfb\u6570\u5168\u90e8\u662f\u6574\u6570\u7684\u591a\u9879\u5f0f\uff0c\u82e5X=q/p\uff08p,q\u4e3a\u4e92\u8d28\u6574\u6570\u65f6\uff09\u8be5\u591a\u9879\u5f0f\u503c\u4e3a\u96f6\uff0c\u5219q\u4e3a\u5e38\u6570\u9879\u7ea6\u6570\uff0cp\u6700\u9ad8\u6b21\u9879\u7cfb\u6570\u7ea6\u6570\uff1b 2\u3001\u5bf9\u4e8e\u591a\u9879\u5f0ff(a)=0,b\u4e3a\u6700\u9ad8\u6b21\u9879\u7cfb\u6570\uff0cc\u4e3a\u5e38\u6570\u9879\uff0c\u5219\u6709a\u4e3ac/b\u7ea6\u6570
\u6362\u5143\u6cd5
\u6709\u65f6\u5728\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u591a\u9879\u5f0f\u4e2d\u7684\u76f8\u540c\u7684\u90e8\u5206\u6362\u6210\u53e6\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u7136\u540e\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6700\u540e\u518d\u8f6c\u6362\u56de\u6765\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53eb\u505a\u6362\u5143\u6cd5\u3002 \u76f8\u5173\u516c\u5f0f
\u6ce8\u610f:\u6362\u5143\u540e\u52ff\u5fd8\u8fd8\u5143. \u4f8b\u5982\u5728\u5206\u89e3(x2+x+1)(x2+x+2)-12\u65f6\uff0c\u53ef\u4ee5\u4ee4y=x^2+x,\u5219 \u539f\u5f0f=(y+1)(y+2)-12 =y^2+3y+2-12=y^2+3y-10 =(y+5)(y-2) =(x^2+x+5)(x2+x-2) =(x^2+x+5)(x+2)(x-1)\uff0e \u4e5f\u53ef\u4ee5\u53c2\u770b\u53f3\u56fe\u3002
\u6c42\u6839\u6cd5
\u4ee4\u591a\u9879\u5f0ff(x)=0,\u6c42\u51fa\u5176\u6839\u4e3ax1\uff0cx2\uff0cx3\uff0c\u2026\u2026xn\uff0c\u5219\u8be5\u591a\u9879\u5f0f\u53ef\u5206\u89e3\u4e3af(x)=(x-x1)(x-x2)(x-x3)\u2026\u2026(x-xn) \uff0e \u4f8b\u5982\u5728\u5206\u89e32x^4+7x^3-2x^2-13x+6\u65f6\uff0c\u4ee42x^4 +7x^3-2x^2-13x+6=0\uff0c \u5219\u901a\u8fc7\u7efc\u5408\u9664\u6cd5\u53ef\u77e5\uff0c\u8be5\u65b9\u7a0b\u7684\u6839\u4e3a0.5 \uff0c-3\uff0c-2\uff0c1\uff0e \u6240\u4ee52x^4+7x^3-2x^2-13x+6=(2x-1)(x+3)(x+2)(x-1)\uff0e
\u56fe\u8c61\u6cd5
\u4ee4y=f(x)\uff0c\u505a\u51fa\u51fd\u6570y=f(x)\u7684\u56fe\u8c61\uff0c\u627e\u5230\u51fd\u6570\u56fe\u50cf\u4e0eX\u8f74\u7684\u4ea4\u70b9x1 ,x2 ,x3 ,\u2026\u2026xn \uff0c\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3af(x)= f(x)=(x-x1)(x-x2)(x-x3)\u2026\u2026(x-xn)\uff0e \u4e0e\u65b9\u6cd5\u247c\u76f8\u6bd4\uff0c\u80fd\u907f\u5f00\u89e3\u65b9\u7a0b\u7684\u7e41\u7410\uff0c\u4f46\u662f\u4e0d\u591f\u51c6\u786e\u3002 \u4f8b\u5982\u5728\u5206\u89e3x^3 +2x^2-5x-6\u65f6\uff0c\u53ef\u4ee5\u4ee4y=x^3; +2x^2 -5x-6. \u4f5c\u51fa\u5176\u56fe\u50cf\uff0c\u4e0ex\u8f74\u4ea4\u70b9\u4e3a-3\uff0c-1\uff0c2 \u5219x^3+2x^2-5x-6=(x+1)(x+3)(x-2)\uff0e
\u4e3b\u5143\u6cd5
\u5148\u9009\u5b9a\u4e00\u4e2a\u5b57\u6bcd\u4e3a\u4e3b\u5143\uff0c\u7136\u540e\u628a\u5404\u9879\u6309\u8fd9\u4e2a\u5b57\u6bcd\u6b21\u6570\u4ece\u9ad8\u5230\u4f4e\u6392\u5217\uff0c\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u7279\u6b8a\u503c\u6cd5
\u5c062\u621610\u4ee3\u5165x\uff0c\u6c42\u51fa\u6570p\uff0c\u5c06\u6570p\u5206\u89e3\u8d28\u56e0\u6570\uff0c\u5c06\u8d28\u56e0\u6570\u9002\u5f53\u7684\u7ec4\u5408\uff0c\u5e76\u5c06\u7ec4\u5408\u540e\u7684\u6bcf\u4e00\u4e2a\u56e0\u6570\u5199\u62102\u621610\u7684\u548c\u4e0e\u5dee\u7684\u5f62\u5f0f\uff0c\u5c062\u621610\u8fd8\u539f\u6210x\uff0c\u5373\u5f97\u56e0\u5f0f\u5206\u89e3\u5f0f\u3002 \u4f8b\u5982\u5728\u5206\u89e3x^3+9x^2+23x+15\u65f6\uff0c\u4ee4x=2\uff0c\u5219 x^3 +9x^2+23x+15=8+36+46+15=105\uff0c \u5c06105\u5206\u89e3\u62103\u4e2a\u8d28\u56e0\u6570\u7684\u79ef\uff0c\u5373105=3\u00d75\u00d77 \uff0e \u6ce8\u610f\u5230\u591a\u9879\u5f0f\u4e2d\u6700\u9ad8\u9879\u7684\u7cfb\u6570\u4e3a1\uff0c\u800c3\u30015\u30017\u5206\u522b\u4e3ax+1\uff0cx+3\uff0cx+5\uff0c\u5728x=2\u65f6\u7684\u503c\uff0c \u5219x^3+9x^2+23x+15\u53ef\u80fd\u7b49\u4e8e(x+1)(x+3)(x+5)\uff0c\u9a8c\u8bc1\u540e\u7684\u786e\u5982\u6b64\u3002
\u5f85\u5b9a\u7cfb\u6570\u6cd5
\u9996\u5148\u5224\u65ad\u51fa\u5206\u89e3\u56e0\u5f0f\u7684\u5f62\u5f0f\uff0c\u7136\u540e\u8bbe\u51fa\u76f8\u5e94\u6574\u5f0f\u7684\u5b57\u6bcd\u7cfb\u6570\uff0c\u6c42\u51fa\u5b57\u6bcd\u7cfb\u6570\uff0c\u4ece\u800c\u628a\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u3002 \u4f8b\u5982\u5728\u5206\u89e3x^4-x^3-5x^2-6x-4\u65f6\uff0c\u7531\u5206\u6790\u53ef\u77e5\uff1a\u8fd9\u4e2a\u591a\u9879\u5f0f\u6ca1\u6709\u4e00\u6b21\u56e0\u5f0f\uff0c\u56e0\u800c\u53ea\u80fd\u5206\u89e3\u4e3a\u4e24\u4e2a\u4e8c\u6b21\u56e0\u5f0f\u3002 \u4e8e\u662f\u8bbex^4-x^3-5x^2-6x-4=(x^2+ax+b)(x^2+cx+d) \u76f8\u5173\u516c\u5f0f
=x^4+(a+c)x^3+(ac+b+d)x^2+(ad+bc)x+bd \u7531\u6b64\u53ef\u5f97a+c=-1\uff0c ac+b+d=-5\uff0c ad+bc=-6\uff0c bd=-4\uff0e \u89e3\u5f97a=1\uff0cb=1\uff0cc=-2\uff0cd=-4\uff0e \u5219x^4-x^3-5x^2-6x-4=(x^2+x+1)(x^2-2x-4)\uff0e \u4e5f\u53ef\u4ee5\u53c2\u770b\u53f3\u56fe\u3002
\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5
\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u5c5e\u4e8e\u56e0\u5f0f\u5206\u89e3\u7684\u4e00\u7c7b\uff0c\u7c7b\u4f3c\u4e8e\u5341\u5b57\u76f8\u4e58\u6cd5\u3002 \u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u5c31\u662f\u4e8c\u5143\u4e8c\u6b21\u516d\u9879\u5f0f\uff0c\u542f\u59cb\u7684\u5f0f\u5b50\u5982\u4e0b: ax^2+bxy+cy^2+dx+ey+f x\u3001y\u4e3a\u672a\u77e5\u6570\uff0c\u5176\u4f59\u90fd\u662f\u5e38\u6570 \u7528\u4e00\u9053\u4f8b\u9898\u6765\u8bf4\u660e\u5982\u4f55\u4f7f\u7528\u3002 \u4f8b\uff1a\u5206\u89e3\u56e0\u5f0f\uff1ax^2+5xy+6y^2+8x+18y+12\uff0e \u5206\u6790\uff1a\u8fd9\u662f\u4e00\u4e2a\u4e8c\u6b21\u516d\u9879\u5f0f\uff0c\u53ef\u8003\u8651\u4f7f\u7528\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002 \u89e3\uff1a\u56fe\u5982\u4e0b\uff0c\u628a\u6240\u6709\u7684\u6570\u5b57\u4ea4\u53c9\u76f8\u8fde\u5373\u53ef x 2y 2 \u2460 \u2461 \u2462 x 3y 6 \u2234\u539f\u5f0f=(x+2y+2)(x+3y+6)\uff0e \u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u5176\u6b65\u9aa4\u4e3a\uff1a \u2460\u5148\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e32\u6b21\u9879\uff0c\u5982\u5341\u5b57\u76f8\u4e58\u56fe\u2460\u4e2dx^2+5xy+6y^2=(x+2y)(x+3y)\uff1b \u2461\u5148\u4f9d\u4e00\u4e2a\u5b57\u6bcd\uff08\u5982y\uff09\u7684\u4e00\u6b21\u7cfb\u6570\u5206\u6570\u5e38\u6570\u9879\u3002\u5982\u5341\u5b57\u76f8\u4e58\u56fe\u2461\u4e2d6y²+18y+12=(2y+2)(3y+6)\uff1b \u2462\u518d\u6309\u53e6\u4e00\u4e2a\u5b57\u6bcd\uff08\u5982x\uff09\u7684\u4e00\u6b21\u7cfb\u6570\u8fdb\u884c\u68c0\u9a8c\uff0c\u5982\u5341\u5b57\u76f8\u4e58\u56fe\u2462\uff0c\u8fd9\u4e00\u6b65\u4e0d\u80fd\u7701\uff0c\u5426\u5219\u5bb9\u6613\u51fa\u9519\u3002 \u5229\u7528\u6839\u4e0e\u7cfb\u6570\u7684\u5173\u7cfb\u5bf9\u4e8c\u6b21\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3 \u4f8b\uff1a\u5bf9\u4e8e\u4e8c\u6b21\u591a\u9879\u5f0f aX^2+bX+c(a\u22600) aX^2+bX+c=a[X^2+(b/a)X+(c/a)X]. \u5f53\u25b3=b^2-4ac\u22650\u65f6\uff0c =a(X^2-X1-X2+X1X2) =a(X-X1)(X-X2).
\u7f16\u8f91\u672c\u6bb5\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u7684\u4e00\u822c\u6b65\u9aa4
\u2460\u5982\u679c\u591a\u9879\u5f0f\u7684\u5404\u9879\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u5148\u63d0\u516c\u56e0\u5f0f\uff1b \u2461\u5982\u679c\u5404\u9879\u6ca1\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u53ef\u5c1d\u8bd5\u8fd0\u7528\u516c\u5f0f\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u5206\u89e3\uff1b \u2462\u5982\u679c\u7528\u4e0a\u8ff0\u65b9\u6cd5\u4e0d\u80fd\u5206\u89e3\uff0c\u90a3\u4e48\u53ef\u4ee5\u5c1d\u8bd5\u7528\u5206\u7ec4\u3001\u62c6\u9879\u3001\u8865\u9879\u6cd5\u6765\u5206\u89e3\uff1b \u2463\u5206\u89e3\u56e0\u5f0f\uff0c\u5fc5\u987b\u8fdb\u884c\u5230\u6bcf\u4e00\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u4e3a\u6b62\u3002 \u4e5f\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u6765\u6982\u62ec\uff1a\u201c\u5148\u770b\u6709\u65e0\u516c\u56e0\u5f0f\uff0c\u518d\u770b\u80fd\u5426\u5957\u516c\u5f0f\u3002\u5341\u5b57\u76f8\u4e58\u8bd5\u4e00\u8bd5\uff0c\u5206\u7ec4\u5206\u89e3\u8981\u5408\u9002\u3002\u201d \u51e0\u9053\u4f8b\u9898 1\uff0e\u5206\u89e3\u56e0\u5f0f(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2\uff0e \u89e3\uff1a\u539f\u5f0f=(1+y)^2+2(1+y)x^2(1-y)+x^4(1-y)^2-2(1+y)x^2(1-y)-2x^2(1+y^2)\uff08\u8865\u9879\uff09 =[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2)\uff08\u5b8c\u5168\u5e73\u65b9\uff09 =[(1+y)+x^2(1-y)]^2-(2x)^2 =[(1+y)+x^2(1-y)+2x][(1+y)+x^2(1-y)-2x] =(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1) =[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)] =(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)\uff0e 2\uff0e\u6c42\u8bc1\uff1a\u5bf9\u4e8e\u4efb\u4f55\u5b9e\u6570x,y\uff0c\u4e0b\u5f0f\u7684\u503c\u90fd\u4e0d\u4f1a\u4e3a33\uff1a x^5+3x^4y-5x^3y^2-15x^2y^3+4xy^4+12y^5\uff0e \u89e3\uff1a\u539f\u5f0f=(x^5+3x^4y)-(5x^3y^2+15x^2y^3)+(4xy^4+12y^5) =x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y) =(x+3y)(x^4-5x^2y^2+4y^4) =(x+3y)(x^2-4y^2)(x^2-y^2) =(x+3y)(x+y)(x-y)(x+2y)(x-2y)\uff0e \uff08\u5206\u89e3\u56e0\u5f0f\u7684\u8fc7\u7a0b\u4e5f\u53ef\u4ee5\u53c2\u770b\u53f3\u56fe\u3002\uff09 \u5f53y=0\u65f6\uff0c\u539f\u5f0f=x^5\u4e0d\u7b49\u4e8e33\uff1b\u5f53y\u4e0d\u7b49\u4e8e0\u65f6\uff0cx+3y\uff0cx+y\uff0cx-y\uff0cx+2y\uff0cx-2y\u4e92\u4e0d\u76f8\u540c\uff0c\u800c33\u4e0d\u80fd\u5206\u6210\u56db\u4e2a\u4ee5\u4e0a\u4e0d\u540c\u56e0\u6570\u7684\u79ef\uff0c\u6240\u4ee5\u539f\u547d\u9898\u6210\u7acb\u3002 3.\uff0e\u25b3ABC\u7684\u4e09\u8fb9a\u3001b\u3001c\u6709\u5982\u4e0b\u5173\u7cfb\u5f0f\uff1a-c^2+a^2+2ab-2bc=0\uff0c\u6c42\u8bc1\uff1a\u8fd9\u4e2a\u4e09\u89d2\u5f62\u662f\u7b49\u8170\u4e09\u89d2\u5f62\u3002 \u5206\u6790\uff1a\u6b64\u9898\u5b9e\u8d28\u4e0a\u662f\u5bf9\u5173\u7cfb\u5f0f\u7684\u7b49\u53f7\u5de6\u8fb9\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002 \u8bc1\u660e\uff1a\u2235-c^2+a^2+2ab-2bc=0\uff0c \u2234(a+c)(a-c)+2b(a-c)=0\uff0e \u2234(a-c)(a+2b+c)=0\uff0e \u2235a\u3001b\u3001c\u662f\u25b3ABC\u7684\u4e09\u6761\u8fb9\uff0c \u2234a\uff0b2b\uff0bc\uff1e0\uff0e \u2234a\uff0dc\uff1d0\uff0c \u5373a\uff1dc\uff0c\u25b3ABC\u4e3a\u7b49\u8170\u4e09\u89d2\u5f62\u3002 4\uff0e\u628a-12x^2n\u00d7y^n+18x^(n+2)y^(n+1)-6x^n\u00d7y^(n-1)\u5206\u89e3\u56e0\u5f0f\u3002 \u89e3\uff1a-12x^2n\u00d7y^n+18x^(n+2)y^(n+1)-6x^n\u00d7y^(n-1) =-6x^n\u00d7y^(n-1)(2x^n\u00d7y-3x^2y^2+1)\uff0e
\u7f16\u8f91\u672c\u6bb5\u56db\u4e2a\u6ce8\u610f
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\u7f16\u8f91\u672c\u6bb5\u5e94\u7528
1\u3001 \u5e94\u7528\u4e8e\u591a\u9879\u5f0f\u9664\u6cd5\u3002 2\u3001 \u5e94\u7528\u4e8e\u9ad8\u6b21\u65b9\u7a0b\u7684\u6c42\u6839\u3002 3\u3001 \u5e94\u7528\u4e8e\u5206\u5f0f\u7684\u901a\u5206\u4e0e\u7ea6\u5206 \u987a\u5e26\u4e00\u63d0\uff0c\u6885\u68ee\u5408\u6570\u5206\u89e3\u5df2\u7ecf\u53d6\u5f97\u4e00\u4e9b\u5fae\u4e0d\u8db3\u9053\u7684\u8fdb\u5c55\uff1a 1\uff0cp=4r+3\uff0c\u5982\u679c8r+7\u4e5f\u662f\u7d20\u6570\uff0c\u5219\uff1a(8r+7)|(2^P-1)\u3002\u5373\uff082p+1\uff09|\uff082^P-1\uff09\uff1b .\u4f8b\u5982\uff1a 23|(2^11-1);\uff1b11=4\u00d72+3\uff1b 47|(2^23-1);\uff1b23=4\u00d75+3\uff1b 167|(2^83-1);,,,.83=4\u00d720+3\uff1b \u3002\u3002\u3002\u3002 2,\uff0cp=2^n\u00d73^2+1,\uff0c\u5219\uff086p+1\uff09|(2^P-1)\uff0c \u4f8b\u5982\uff1a223|(2^37-1);\uff1b37=2\u00d72\u00d73\u00d73+1\uff1b 439|(2^73-1)\uff1b73=2\u00d72\u00d72\u00d73\u00d73+1\uff1b 3463|(2^577-1);\uff1b577=2\u00d72\u00d72\u00d72\u00d72\u00d72\u00d73\u00d73+1\uff1b \uff0c\uff0c\uff0c\u3002 3\uff0cp=2^n\u00d73^m\u00d75^s-1,\u5219\uff088p+1\uff09|\uff082^P-1\uff09\uff1b .\u4f8b\u5982;233|(2^29-1)\uff1b29=2\u00d73\u00d75-1\uff1b ;1433|(2^179-1)\uff1b179=2\u00d72\u00d73\u00d73\u00d75-1\uff1b 1913|\uff082^239-1\uff09\uff1b239=2\u00d72\u00d72\u00d72\u00d73\u00d75-1\uff1b \uff0c\uff0c\uff0c\u3002 \u8fd8\u6709\u4e00\u4e9b\u6885\u68ee\u6570\u5206\u89e3\u53d6\u5f97\u8fdb\u5c55\uff0c\u4e0d\u518d\u4e00\u4e00\u53d9\u8ff0
1、提取公因式法，把各项中的公因式或公因数提取，特别不让人注意的因数往往被
人忽略；
2、完全平方公式：项数——三项，
满足完全平方公式——(a±b)^2=a^2±2ab+b^2。
3、平方差公式：项数——两项，
满足两式平方公式的形式——a^2-b^2=(a+b)(a-b).
4、任何一个因式分解题先看是否有公因式(数)可提取，
然后再项数确定是否符合公式。
绛旓細1銆佹彁鍙栧叕鍥犲紡娉锛屾妸鍚勯」涓殑鍏洜寮忔垨鍏洜鏁版彁鍙栵紝鐗瑰埆涓嶈浜烘敞鎰忕殑鍥犳暟寰寰琚 浜哄拷鐣ワ紱2銆佸畬鍏ㄥ钩鏂瑰叕寮忥細椤规暟鈥斺斾笁椤癸紝婊¤冻瀹屽叏骞虫柟鍏紡鈥斺(a卤b)^2=a^2卤2ab+b^2銆3銆佸钩鏂瑰樊鍏紡锛氶」鏁扳斺斾袱椤癸紝婊¤冻涓ゅ紡骞虫柟鍏紡鐨勫舰寮忊斺攁^2-b^2=(a+b)(a-b).4銆佷换浣曚竴涓洜寮忓垎瑙ｉ鍏堢湅鏄惁鏈...
绛旓細浜斻佹崲鍏冩硶 鏈夋椂鍦ㄥ垎瑙ｅ洜寮忔椂锛屽彲浠ラ夋嫨澶氶」寮忎腑鐨勭浉鍚岀殑閮ㄥ垎鎹㈡垚鍙︿竴涓湭鐭ユ暟锛岀劧鍚庤繘琛屽洜寮忓垎瑙ｏ紝鏈鍚庡啀杞崲鍥炴潵锛岃繖绉嶆柟娉曞彨鍋氭崲鍏冩硶銆傛敞鎰忥細鎹㈠厓鍚庡嬁蹇樿繕鍏.鍏佹眰鏍瑰叕寮忔硶 浠ゅ椤瑰紡f(x)=0,姹傚嚭鍏舵牴涓簒1锛寈锛寈3锛屸︹n锛屽垯璇ュ椤瑰紡鍙垎瑙ｄ负f(x)=(x-x1)(x-x2)(x-x3)鈥︹(x-xn)涓...
绛旓細鍒嗙粍鍒嗚В娉 瑕佹妸澶氶」寮廰m+an+bm+bn鍒嗚В鍥犲紡锛鍙互鍏堟妸瀹冨墠涓ら」鍒嗘垚涓缁勶紝骞舵彁鍑哄叕鍥犲紡a锛屾妸瀹冨悗涓ら」鍒嗘垚涓缁勶紝骞舵彁鍑哄叕鍥犲紡b锛屼粠鑰屽緱鍒癮(m+n)+b(m+n),鍙堝彲浠ユ彁鍑哄叕鍥犲紡m+n锛屼粠鑰屽緱鍒(a+b)(m+n) 渚3銆佸垎瑙ｅ洜寮弇 +5n-mn-5m 瑙ｏ細m +5n-mn-5m= m -5m -mn+5n = (m -5m )+(...
绛旓細1銆=a(x+y)鐨勫钩鏂-b锛坸+y)(x-y)=(x+y)[a(x+y)-b(x-y)]=(x+y)(ax+ay-bx+by)2銆=浜屽垎涔嬩竴a(a鐨勫钩鏂-8a+16)=浜屽垎涔嬩竴a(a-4)鐨勫钩鏂 3銆=2锛坸鐨勫钩鏂+x+1/4)=2(x+1/2)鐨勫钩鏂 4銆=x鐨勫钩鏂+3x+2+1/4=x鐨勫钩鏂+3x+9/4=(x+3/2)鐨勫钩鏂 ...
绛旓細(1/4x^2-xy+y^2)/(x-2y)=(x^2-4xy+4y^2)/4(x-2y)=(x-2y)(x-2y)/4(x-2y)=(x-2y)/4 (x-1)^2=(x-1)(x+1)瑙锛(x-1)^2-(x-1)(x+1)=0 (x-1)[(x-1)-(x+1)]=0 (x-1)脳(-2)=0 x-1=0 x=1 9^13-3^24 =9^13-9^12 =9脳9^12-9^12 =8...
绛旓細锛1锛6*x鐨勫钩鏂+5xy-6*y鐨勫钩鏂-6xz+4yz =(3x-2y)*(2x+3y)-2z*(3x-2y)=(3x-2y)*(2x+3y-2z)锛2锛墄鐨勫钩鏂-xy+2x+y-3 =(x^2+3x-4)-(xy+x)+(y+1)=(x-1)(x+4)-x(y+1)+(y+1)=(x-1)(x+4)-(y+1)(x-1)=(x-1)(x-y+3)...
绛旓細1.鍘熷紡=锛2X+Y锛夛紙2X-3Y+X锛=锛2X+Y锛夛紙3X-3Y锛=3锛2X+Y锛夛紙X-Y锛2.鍘熷紡=Y锛圶-Y锛夌殑骞虫柟+锛圶-Y锛夌殑绔嬫柟=锛圶-Y锛夌殑骞虫柟*锛圷+X-Y锛=锛圶-Y锛夌殑骞虫柟*X 3.鍥犱负X鐨勫钩鏂+3X+5=7 鎵浠鐨勫钩鏂+3X=7-5=2 鍥犱负3X鐨勫钩鏂+9X-2=3*锛圶鐨勫钩鏂+3X锛-2 鎵浠ョ瓑浜3*2-...
绛旓細锛1锛 锛坅+b锛²+6锛坅+b锛+9=[(a+b)+3]²=(a+b+3)²锛2锛 16 -24锛坸-y锛+9锛坸-y锛²=[4-3(x-y)]²=(4-3x+3y)²
绛旓細1.鍒嗚В鍥犲紡(1+y)-2x(1+y)+x(1-y) 瑙:鍘熷紡=(1+y)+2(1+y)+x(1-y)+x(1-y)-2(1+y)x(1-y)-2x(1+y) =[(1+y)+x(1-y)]-2(1+y)x(1-y)-2x(1+y) =[(1+y)+x(1-y)]-(2x) =[(1+y)+x(1-y)+2x]路[(1+y)+x(1-y)-2x] =(x-xy+2x+y+1)(x-xy-2x+y...
绛旓細1.[1-锛4a²锛²]/(4a²+1)(2a+1锛=锛4a²+1)(2a+1)(1-2a)/(4a²+1)(2a+1锛=1-2a 2.锛3a-4锛²=25 3a-4=卤5 瑙ｅ緱a1=9/3 锛宎2=-1/3
