分解因式x^4-3x+1 x^4+4 x^4-23x^2y^2+y^4 x^4+64y^4 a^3-3a+2 x^3+x
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分解因式x^4-3x+1 x^4+4 x^4-23x^2y^2+y^4 x^4+64y^4 a^3-3a+2 x^3+x+30求解,要十分详细的
最好是带方法名字例如十字相乘分组分解公式法等等,追分 急
最好是带方法名字例如十字相乘分组分解公式法等等,追分 急
![分解因式x^4-3x+1 x^4+4 x^4-23x^2y^2+y^4 x^4+64y^4 a^3-3a+2 x^3+x](/uploads/image/z/17369997-69-7.jpg?t=%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8Fx%5E4-3x%2B1+x%5E4%2B4+x%5E4-23x%5E2y%5E2%2By%5E4+x%5E4%2B64y%5E4+a%5E3-3a%2B2+x%5E3%2Bx)
是x^4-3x^2+1;x^4+4;x^4-23x^2·y^2+y^4;x^4+64y^4; a^3-3a+2;x^3+x+30吧.
`
x^4-3x^2+1
=x^4-2x^2+1-x^2
=(x^2+1)^2-x^2
=(x^2+x+1)(x^2-x+1)
`
x^4+4
=x^4+4x^2+4-4x^2
=(x^2+2)^2-(2x)^2
=(x^2+2x+2)(x^2-2x+2)
`
x^4-23x^2 y^2+y^4
=x^4-2x^2 y^2+y^4-25x^2 y^2
=(x^2-y^2)^2-(5xy)^2
=(x^2-5xy-y^2)(x^2+5xy-y^2)
`
x^4+64y^4
=x^4+16x^2 y^2+64y^4-16x^2 y^2
=(x^2+8y^2)^2-(4xy)^2
=(x^2-4xy+8y^2)(x^2+4xy+8y^2)
`
a^3-3a+2
=(a^3-a^2)+(a^2-a)-2(a-1)
=(a^2+a-2)(a-1)
=[a(a-1)+2(a-1)](a-1)
=(a+2)(a-1)(a-1)
=(a+2)(a-1)^2
`
x^3+x+30
=x^3+3x^2-3x^2-9x+10x+30
=x^2(x+3)-3x(x+3)+10(x+3)
=(x^2-3x+10)(x+3)
`
`
x^4-3x^2+1
=x^4-2x^2+1-x^2
=(x^2+1)^2-x^2
=(x^2+x+1)(x^2-x+1)
`
x^4+4
=x^4+4x^2+4-4x^2
=(x^2+2)^2-(2x)^2
=(x^2+2x+2)(x^2-2x+2)
`
x^4-23x^2 y^2+y^4
=x^4-2x^2 y^2+y^4-25x^2 y^2
=(x^2-y^2)^2-(5xy)^2
=(x^2-5xy-y^2)(x^2+5xy-y^2)
`
x^4+64y^4
=x^4+16x^2 y^2+64y^4-16x^2 y^2
=(x^2+8y^2)^2-(4xy)^2
=(x^2-4xy+8y^2)(x^2+4xy+8y^2)
`
a^3-3a+2
=(a^3-a^2)+(a^2-a)-2(a-1)
=(a^2+a-2)(a-1)
=[a(a-1)+2(a-1)](a-1)
=(a+2)(a-1)(a-1)
=(a+2)(a-1)^2
`
x^3+x+30
=x^3+3x^2-3x^2-9x+10x+30
=x^2(x+3)-3x(x+3)+10(x+3)
=(x^2-3x+10)(x+3)
`
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