1.x^3-3x+22.3x^3+7x^2-43.y^5-11y^3+y4.a^2-4ab+3b^2+2bc-c^25.a^4+a^2b^2+b^46.4x^4+1(7)x^4+4y^47.a^5+a+18.x^3+6x^2+11x+610.x^3-9x+8
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1.x^3-3x+22.3x^3+7x^2-43.y^5-11y^3+y4.a^2-4ab+3b^2+2bc-c^25.a^4+a^2b^2+b^46.4x^4+1(7)x^4+4y^47.a^5+a+18.x^3+6x^2+11x+610.x^3-9x+8
1.x^3-3x+2
2.3x^3+7x^2-4
3.y^5-11y^3+y
4.a^2-4ab+3b^2+2bc-c^2
5.a^4+a^2b^2+b^4
6.4x^4+1(7)x^4+4y^4
7.a^5+a+1
8.x^3+6x^2+11x+6
10.x^3-9x+8
1.x^3-3x+22.3x^3+7x^2-43.y^5-11y^3+y4.a^2-4ab+3b^2+2bc-c^25.a^4+a^2b^2+b^46.4x^4+1(7)x^4+4y^47.a^5+a+18.x^3+6x^2+11x+610.x^3-9x+8
1
x^3-3x+2
=(x^3-1)-3x+3
=(x-1)(x^2+x+1)-3(x-1)
=(x-1)(x^2+x-2)
=(x-1)(x-1)(x+2)
2
3x^3+7x^2-4=(3x^3+3x^2)+(4x^2-4)
=3x^2(x+1)+4(x^2-1)
=3x^2(x+1)+4(x+1)(x-1)
=(x+1)(3x^2+4x-4)
=(x+1)(x+2)(3x-2)
3
原式=y（y^4-2y^2+1-9y^2） =y[（y^2-1）^2-9y^2] =y（y^2+3y-1）（y^2-3y-1）
4
原式=a^2-4ab+4b^2-b^2+2bc-c^2 =(a-2b)^2-(b^2-2bc+c^2) =(a-2b)^2-(b-c)^2 =(a-2b+b-c)(a-2b-b+c) =(a-b-c)(a-3b+c)
=a^2 x^2+2axby+b^2 y^2+b^2 x^2-2aybx+a^2 y^2
=a^2 x^2+b^2 y^2+b^2 x^2+a^2 y^2
=a^2（x^2+y^2）+b^2（x^2+y^2）
=（a^2+b^2）（x^2+y^2）
5
a^4+a^2b^2+b^4=(a^2+b^2)^2-a^2b^2=(a^2+b^2-ab)(a^2+b^2+ab)
7
a^5+a+1 =a^5+a^4+a^3 -a^4-a^3-a^ +a^+a+1 =(a^+a+1)(a^3-a^+1)
8
x^3+6x^2+11x+6
=x^3+6x^2+9x+2x+6
=x(x+3)^2+2(x+3)
=(x^2+3x+2)(x+3)
=（x+1）（x+2）（x+3)
10
x^3-9x+8
解法1.x^3-9x+8
=x^3-1-9x+9
=(x-1)(x^2+x-8)
解法2.x^3-9x+8
=x^3-x-8x+8
=(x-1)(x^2+x-8)
解法3.x^3-9x+8
=9x^3-8x^3-9x+8
=(x-1)(x^2+x-8)
解法4.x^3-9x+8
=x^3-x^2+x^2-9x+8
=x^2(x-1)+(x-8)(x-1)
最后一个 6.4x^4+1(7)x^4+4y^4 中