Observation

This question was also reported to be very popular among the candidates and majority of them performed well in it. Majority of them were reported to recall that every polynomial, P(x) can be expressed as P(x) = Quotient × Divisor + Remainder. In this case, the quotient was (2x – 5), the divisor was (x2 + 5x + 1) and the remainder was (30x + 16). Therefore, 2x3 + mx2 + nx + 11 = (2x – 5)(x2 + 5x + 1) + (30x + 16). Simplifying the left hand side of the equation gave 2x3 + 5x2 + 7x + 11. Comparing this expression with the given expression gave m = 5 and n = 7.