Question

当K为何值时,多项式x^2-2xy-3y^2+3x-5y+k能分解成两个一次因式的积

Answer 1

x^2-2xy-3y^2+3x-5y+k

=(x-3y)(x+y)+3x-5y+k

=(x-3y)(x+y)+2x-6y+x+y+k

=(x-3y)(x+y)+2(x-3y)+(x+y)+k

=(x-3y)(x+y+2)+(x+y+2)+k-2

=(x-3y+1)(x+y+2)+k-2

所以：当k-2=0,即k=2时,多项式能分解成两个一次因式的积