当k=_时,kx2-2xy-3y2+3x-5y+2能分解成两个一次因式的积是_.

问题描述:

当k=______时,kx2-2xy-3y2+3x-5y+2能分解成两个一次因式的积是______.

∵kx2-2xy-3y2+3x-5y+2
=kx2-(2y-3)x-3y2-5y+2
=kx2-(2y-3)x-(y+2)(3y-1)
=(x+y+2)(x-3y+1),
即只有k=1时,kx2-2xy-3y2+3x-5y+2才能分解成两个一次因式的积是(x+y+2)(x-3y+1).
故答案为:1,(x+y+2)(x-3y+1).