The correct option is C 16
From remainder theorem, we know
The remainder when p(x) is divided by x−1, the remainder is p(1)
∴
p(1)=12+3(1)+1=1+3+1=5
Similarly,
The remainder when p(x) is divided by x−2, the remainder is p(2)
∴
p(2)=22+3(2)+1=4+6+1=11
∴ The sum of remainders = 5 + 11 = 16