若3x²-kx+4被3x-1除后余3,则k=_

问题描述:

若3x²-kx+4被3x-1除后余3,则k=_

因二次项系数为3,则设商为X+A
(3X-1)×(X+A)+3
=3X²-X+3AX-A+3
=3X²-(1-3A)X+(3-A)
3-A=4
则A=-1
把A=-1代入1-3A中,得
1-3A=1+3=4
则K=4