Problem: Let the expression x2+3x+2 have a remainder of zero when divided by 6, and let S be the set of integers {0,1,2,…,25}. The number of members of S satisfying the given condition is:
Answer Choices:
A. 25
B. 22
C. 21
D. 18
E. 17
Solution:
x2+3x+2=(x+2)(x+1)=(x+4)(x+5)=0. If x+2=0,x=4; if x+1=0,x=5; if x+4=0, x=2; if x+5;0,x=1. Additional values of x are, respectively, 10,11,8,7, and so forth.