Problem:
If f(x)=x(x+1)(x+2)(x+3) then f(0)+f(−1)+f(−2)+f(−3)=
Answer Choices:
A. −8/9
B. 0
C. 8/9
D. 1
E. 10/9
Solution:
Since 0z=0 for any z>0,f(0)=f(−2)=0. Since (−1)0=1, f(0)+f(−1)+f(−2)+f(−3)=(−1)0(1)2+(−3)−2(−1)0=1+(−3)21​=910​.