Let f(x) be the given polynomial and when f(x) is divided by x² – 2x – 3, let the quotient be Q(x) and the remainder be ax + b.

\ f(x) = Q(x)(x² – 2x – 3) + ax + b

put x = 1 ; f(–1) = a(–1) + b

–1 = –a + b –––––––––(1)

put x = 3 ; f(3) = a(3) + b

7 = 3a + b –––––––––(2)

solving (1) and (2), a = 2 ; b = 1

\ Remainder is 2x + 1 Choice (4)