分组分解法x^2-y^2-z^2+2yz+x+y-z必须用分组分解法,其他方法不需要.①x^2-y^2-z^2+2yz+x+y-z②a^4-3a^2+9③x^3-4x^2+5x-2

Question

分组分解法 x^2-y^2-z^2+2yz+x+y-z
必须用分组分解法,其他方法不需要.
①x^2-y^2-z^2+2yz+x+y-z
②a^4-3a^2+9
③x^3-4x^2+5x-2

Answer 1

①x^2-y^2-z^2+2yz+x+y-z
=x²-(y²-2yz+z²)+(x+y-z)
=x²-(y-z)²+(x+y-z)
=(x+y-z)(x-y+z)+(x+y-z)
=(x+y-z)(x-y+z+1)

②a^4-3a^2+9
=a^4+6a²+9-9a²
=(a^4+6a²+9)-9a²
=(a²+3)²-(3a)²
=(a²+3a+3)(a²-3a+3)

③x^3-4x^2+5x-2
=(x²-4x+4x)+(x-2)
=x(x-2)²+(x-2)
=(x-2)(x²-2x+1)
=(x-2)(x-1)²