高一数学因式分难解题集锦.ppt

因式分解 高一难题集锦 说明： 本课件不同于其他因式分解系列课件。 本课件在因式分解基础之上逐步提升一层。 包含各类因式分解难题，错题。 请讲解完因式分解基础部分再使用本课件。 感谢！ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 试着因式分解下列难题！ bc(b+c)+ca(c-a)-ab(a+b) n提示： n运用加减因式来完成此 题 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n=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) n当遇到实在无法解出的题目，可以尝试 用这个方法！ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 试着因式分解下列难题！ (x2+x+1)(x2+x+2)-12 n提示 n尝试换元解决此题 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n可以令y=x2+x,则 原式=(y+1)(y+2)-12 =y2+3y+2-12=y2+3y-10 =(y+5)(y-2) =(x2+x+5)(x2+x-2) =(x2+x+5)(x+2)(x-1) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 试着因式分解下列难题！ (1+y)2-2x2(1+y2)+x4(1-y)2 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n原式=(1+y)2+2(1+y)x2(1+y)+x4(1- y)2-2(1+y)x2(1-y)-2x2(1+y2) =(1+y)+x2(1-y)2-2(1+y)x2(1-y)- 2x2(1+y2) =(1+y)+x2(1-y)2-(2x)2 =(1+y)+x2(1-y)+2x(1+y)+x2(1-y)- 2x =(x2-x2y+2x+y+1)(x2-x2y-2x+y+1) =(x+1)2-y(x2-1)(x-1)2-y(x2-1) =(x+1)(x+1-xy+y)(x-1)(x-1-xy-y) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 试着因式分解下列难题！ nx5+3x4y-5x3y2+4xy4+12y5 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n原式=(x5+3x4y)- (5x3y2+15x2y3)+(4xy4+12y5 ) =x4(x+3y)- 5x2y2(x+3y)+4y4(x+3y) =(x+3y)(x4-5x2y2+4y4) =(x+3y)(x2-4y2)(x2-y2) =(x+3y)(x+y)(x-y)(x+2y)(x-2y) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 试着因式分解下列难题！ n1.(2a-b)+8ab 2.y-2y-x+1 3.x-xy+yz-xz 4.6x+5x-4 5.2a-7ab+6b n看你需要多少时间解完以上小题。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n答案：1.(2a-b)+8ab=(2a+b) 2.y-2y-x+1=(y-1)-x=(y-1-x)(y-1+x) 3.x-xy+yz-xz =x(x-y)-z(x-y)=(x- z)(x-y) 4.6x+5x-4 =(2x-1)(3x+4) 5.2a-7ab+6b=(2a-3b)(a-2b) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. n6.(x-2x)+2(x-2x)+1 7.(x-2x)-14(x-2x)-15 8.x(x-y)+(y-x) 9.169(a+b)-121(a-b) 10.(x-3)(x-5)+1 试着因式分解下列难题！ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n6.(x-2x)+2(x-2x)+1 =(x-2x+1)=(x-1)4 7.(x-2x)-14(x-2x)-15 =(x-2x-15)(x- 2x+1)=(x+3)(x-5)(x-1) 8.x(x-y)+(y-x) =(x-1)(x-y)=(x+1)(x-1)(x-y) 9.169(a+b)-121(a-b) =(14a+14b-11a+11b)(14a+14b+11a-11b) =(3a+25b)(25a+3b) 10.(x-3)(x-5)+1 =(x-3)-2(x-3)+1 =(x-3- 1)=(x-4) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. n因式分解9x230x25 n因式分解20x29x20 n因式分解12x229x15 n因式分解36x239x9 n因式分解21x231x22 n用十字相乘解决以上问题！ 试着因式分解下列难题！ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n因式分解9x230x25(3x-5)2 因式分解20x29x20(-4x+5)(5x+4) 因式分解12x229x15(4x-3)(3x-5) 因式分解36x239x93(3x+1)(4x+3) 因式分解21x231x22(21x+11)(x-2) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. n因式分解9x435x24 n因式分解(2x1)(x1)(2x1)(x 3) n因式分解2ax23x2ax3 n因式分解x(y2)xy1 n因式分解(x23x)(x3)2 n用十字相乘解决以上问题！ 试着因式分解下列难题！ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 解法（仔细思考后再对照答案 ） n因式分解9x435x24(9x2+1)(x+2)(x-2) 因式分解(2x1)(x1)(2x1)(x3) 2(x-1)(2x+1) 因式分解2ax23x2ax3(x+1)(2ax-3) 因式分解x(y2)xy1(x-1)(y+1) 因式分解(x23x)(x3)2(x-3)(2x-3) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 思考题 n因式分解9x535x34x Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 思考题答案 nx(9x2+1)(x+2)(x-2) Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 课后作业 因式分解82x2 因式分解x41 因式分解x24xxy2y4 因式分解4x212x5 因式分解21x231x22 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.