x4+ax3-(2a2+1)x2-ax+2a2因式分解

(1)x4+ax3-(2a2+1)x2-ax+2a2
=x^4+ax^3-2a^2*x^2-x^2-ax+2a^2
=(x^4-x^2)+(ax^3-ax)-(2a^2*x^2-2a^2)
=x²(x²-1)+ax(x²-1)-2a²(x²-1)
=(x²-1)(x²+ax-2a²)
=(x+1)(x-1)(x+2a)(x-a)
(2)2x²+5xy-3y²-3x+5y-2
∵2x²+5xy-3y²=(2x-y)(x+3y)
设2x²+5xy-3y²-3x+5y-2=(2x-y+a)(x+3y+b)=2x²+5xy-3y²+(a+2b)x+(b-3a)y+ab
∴a+2b=-3①,3a-b=5② ab=-2③
由①②得a=1,b=-2,代入③成立,
∴2x²+5xy-3y²-3x+5y-2=(2x-y+1)(x+3y-2)

x4+ax3-(2a2+1)x2-ax+2a2
==x^4+ax^3-2a^2*x^2-x^2-ax+2a^2
=(x^4-x^2)+(ax^3-ax)-(2a^2*x^2-2a^2)
=x^2(x^2-1)+ax(x^2-1)-2a^2(x^1-1)
=(x^2-1)(x^2+ax-2a^2)
=(x+1)(x-1)(x+2a)(x-a)