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1、因式分解之四十字相乘法答案十字相乘法 答案 例题1： x2-3x-10=(x-5)(x+2) 12711x+x+3=-(x2-7x-18)=-(x-9)(x+2) 6666-x2+2x+15=-(x2-2x-15)-(x-5)(x+3) -x2-5xy+6y2=(x-2y)(x-3y) x2-5xy-6y2=(x-6y)(x+y) 3x2-11x+10=(3x-5)(x-2) -2x2+15x-7=-(2x2-15x+7)=-(2x-1)(x-7) 3x2-2xy-8y2(3x+4y)(x-2y) 2x2-7x+3=(2x-1)(x-3) 6-5x+x2=(x-2)(x-3) 例题2： 18x
2、2-19x+5=(2x-1)(9x-5) x2-4x-5=(x-5)(x+1) x2-7xy+10y2=(x-2y)(x-5y) x2-2x-15=(x-5)(x+3) 3x2-7x-40=(3x+8)(x-5) 2x2-x-15=(2x+5)(x-3) 2x2+7x-15=(2x-3)(x+5) x2-9x-52=(x-13)(x+4) x2+xy-6y2=(x+3y)(x-2y) (3x-1)(2x-3)+1=6x2-11x+4 例题3： x+2x-24=(x+6)(x-4) x+15x+36=(x+3)(x+12) 6x-7x-3=(3x+1)(2x-3) 4x+x-3=(4x-3)(x
3、+1) 2x+15x+7=(2x+1)(x+7) 4x-5x-6=(4x+3)(x-2) x+29xy+100y=(x+25y)(x+4y) 15x+7xy-4y=(3x-y)(5x+4y) 12x-11x-15=(3x-5)(4x+3) x-3x+2=(x-1)(x-2) 例题4： -x+13x-36=-(x-4)(x-9) -x+5x+14=-(x-7)(x+2) 1 2222222222222212411x-x-7=(x2-4x-21)=(x-7)(x+3) 333351122x+x-1=(6x+5x-6)=(3x-2)(2x+3) 666111122-a+a-6=-(2a-11a+12
4、)=-(2a-3)(a-4) 2225211222-6x+7xy-y=-(18x-21xy+5y)=-(3x-y)(6x-5y) 333a4-5a2-14=(a2-7)(a2+2) ab2+2ab-3a=a(b+3)(b-1) x2-9x-10=(x-10)(x+1) x2+4x-12=(x+6)(x-2) 例题5： (x+y)2-4(x+y)-12=(x+y-6)(x+y+2) x6+19x3-216=(x3+27)(x3-8)=(x+3)(x2-3x+9)(x-2)(x2+2x+4) 12(x+y)2+11(x+y)(x-y)+2(x-y)2=(3x+3y-2x+2y)(4x+4y+x-y
5、) =(x+5y)(5x+3y) (x+x)-17(x+x)-60=(x+x-20)(x+x+3)=(x+5)(x-4)(x+x+3) (x+2x)-7(x+2x)-8=(x+2x-8)(x+2x+1)=(x+4)(x-2)(x+1) (2a+b)-14(2a+b)+48=(2a+b-6)(2a+b-8) (x-y)-5(x-y)-36=(x-y-9)(x-y+4) (a+b)+2a+2b-3=(a+b+3)(a+b-1) x-2xy+y-x+y-6=(x-y)-(x-y)-6=(x-y-3)(x-y+2) a-b+4a+2b+3=(a+b)(a-b)+4a+2b+3 222222222222
6、22222222=(a+b+1)(a-b+3) 例题6： xy+y+x-y-2=y(x+y)+x-y-2=(y+1)(x+y-2) x-10xy+25y+6x-30y+8=(x-5y)-6(x-5y)+8 2222=(x-5y+2)(x-5y+4) x2+xy-6y2+x+13y-6=(x+3y)(x-2y)+x+13y-6 =(x+3y-2)(x-2y+3) (a+3a)-2(a+3a)-8=(a+3a-4)(a+3a+2) 22222=(a+4)(a-1)(a+1)(a+2) (x+x-1)-4x-4x+7=(x+x-1)-4(x+x-1)+3 222222=(x2+x-1+1)(x2+x
7、-1+3)=(x2+x)(x2+x+2)=x(x+1)(x2+x+2) 2(x-y)-2(x-y)-8=(x-y-4)(x-y+2) 22x-xy-2y-x-7y-6=(x-2y)(x+y)-x-7y-6 =(x-2y-2)(x+y+3) 3(x+1)-8(x+1)+4=(3x+3-2)(x+1-2)=(3x+1)(x-1) 2 23(m+n)3-2(m+n)2-5(m+n)=(m+n)3(m+n)2-2(m+n)-5 =(m+n)(3m+3n-5)(m+n+1) x2+xy-2y2+2x+7y-3=(x+2y)(x-y)+2x+7y-3 =(x+2y-1)(x-y+3) 例题7： x(x-1
8、)(x-2)(x-3)+1=(x2-3x)(x2-3x+2)+1 =(x2-3x)2+2(x2-3x)+1=(x2-3x+1)2 (x2+x-6)(x2+5x-6)-5x2=(x2-6)2+6x(x2-6)=(x2-6)(x2-6-6x) (x+3)(x-5)(x+6)(x-10)-20x2 =(x2-30-7x)(x2-30+x)-20x2=(x2-30)2-6x(x2-30)-27x2=(x-9x-30)(x+3x-30)(x2+xy+y2)(x2+xy+2y2)-12y4 =(x2+xy+y2)2+y2(x2+xy+y2)-12y4=(x2+xy+y2+4y2)(x2+xy+y2-3y2
9、) =(x2+xy+5y2)(x+2y)(x-y)(x+2x)(x+2x-2)-3=(x+2x)-2(x+2x)-3 2222222=(x2+2x-3)(x2+2x+1)=(x+3)(x-1)(x+1)2 22222(x+5x+6)(x+5x-2)-9=(x+5x)+4(x+5x)-21 =(x2+5x+7)(x2+5x-3) 22(x-1)(x-2)(x-3)(x-4)-3=(x-5x+4)(x-5x+6)-3 =(x2-5x)2+10(x2-5x)+21=(x2-5x+7)(x2-5x+3) 22222(x+3x-2)(x+3x+4)-16=(x+3x)+2(x+3x)-24 =(x2+3
10、x+6)(x2+3x-4)=(x2+3x+6)(x+4)(x-1) 22(x+1)(x+2)(x+3)(x+4)-35=(x+5x+4)(x+5x+6)-35 =(x2+5x)2+10(x2+5x)-11=(x2+5x+11)(x2+5x-1) 22222(x+x+1)(x+x+2)-12=(x+x)+3(x+x)-10 =(x2+x+5)(x2+x-2)=(x2+x+5)(x+2)(x-1) 例题8： (x+3)(x-1)(x+5)-20 2=(x+1)(x-1)(x+3)(x+5)-20=(x2+4x)+3(x2+4x)-5-20=(x2+4x)2-2(x2+4x)-35=(x2+4x-7
11、)(x2+4x+5)22(x+3x+2)(4x+8x+3)-90 =(x+1)(x+2)(2x+1)(2x+3)-90=(2x2+5x+3)(2x2+5x+2)-90=(2x2+5x)2+5(2x2+5x)-84 =(2x2+5x+12)(2x2+5x-7)22x-3xy-10y+x+9y-2=(x-5y)(x+2y)+x+9y+2 =(x-5y+2)(x+2y-1) 3 (x2+4x) x2-y2+5x+3y+4=(x+y)(x-y)+5x+3y+4 =(x+y+1)(x-y+4) 6x2-7xy-3y2-xz+7yz-2z2=(3x+y)(2x-3y)-z(x-7y)-2z2 =(3x+y
12、-2z)(2x-3y+z) x2-8xy+15y2+2x-4y-3=(x-3y)(x-5y)+2x-4y-3 =(x-3y-1)(x-5y+3) x2-xy+2x+y-3=x(x-y)+2x+y-3 =(x-1)(x-y+3) 解法二： x2-xy+2x+y-3=(x+3)(x-1)-y(x-1)=(x-1)(x+3-y) 3x2-11xy+6y2-xz-4yz-2z2=(3x-2y)(x-3y)-z(x+4y)-2z2 =(3x-2y+2z)(x-3y-z) 2x2+3xy-9y2+14x-3y+20=(2x-3y)(x+3y)+14x-3y+20 =(2x-3y+4)(x+3y+5) x2+3xy+2y2+4x+5y+3=(x+y)(x+2y)+4x+5y+3 =(x+y+1)(x+2y+3) 4
