Vivekanand Vellanki
2

Option 4 is correct.


Lets see how. Let's define a new polynomial f(x) = p(x) + 2.


Clearly, f(3) = p(3) + 2 = -2 + 2 = 0.


From reminder theorem, (x - 3) is a factor of f(x). This means that

f(x) = (x - 3)g(x)

p(x) + 2 = (x - 3)g(x); or

p(x) = (x - 3)g(x) - 2


So, when p(x) is divided by (x - 3), we get a reminder of -2.