When (f(x) = 2x^{3} + mx^{2} + nx + 11) is divided by (x^{2} + 5x + 1), the quotient is (2x – 5) and the remainder is (30x + 16). Find the values of m and n.
Explanation
To get f(x), multiply the divisor with the quotient and add the remainder.
(2x^{3} + mx^{2} + nx + 11 = (x^{2} + 5x + 1)(2x – 5) + (30x + 16))
= (2x^{3} – 5x^{2} + 10x^{2} – 25x + 2x – 5 + 30x + 16)
= (2x^{3} + 5x^{2} + 7x + 11)
Therefore, m = 5 and n = 7.