参考答案: D
详细解析:
由题可知,(x-1),(x-2 ),(x+3 )均为f(x)的因式,则设f(x)=a(x-1)(x-2 )(x+3 ),又因为f(0)=a(0-1)(0-2 )(0+3 )=6,得到a=1,因此f(x)=(x-1)(x-2 )(x+3 ),f(-1)=(-1-1)(-1-2 )(-1+3 )=12
若三次多项式f(x)满足 f(1)=f(2)=f(-3)=0,f(0)=6,则f(-1)=( )。
A. 0
B. 1
C. -1
D. 12
E. 24
参考答案: D
详细解析:
由题可知,(x-1),(x-2 ),(x+3 )均为f(x)的因式,则设f(x)=a(x-1)(x-2 )(x+3 ),又因为f(0)=a(0-1)(0-2 )(0+3 )=6,得到a=1,因此f(x)=(x-1)(x-2 )(x+3 ),f(-1)=(-1-1)(-1-2 )(-1+3 )=12