Let f(x) = x⁴ + px³ + qx + 5 where p, q are constants.

The remainder when f(x) is divided by (x + 1) is 7, and the remainder when f(x) is divided by (x − 2) is 1. Find the value of p and the value of q.

attempt to substitute x = −1 or x = 2 or to divide polynomials      (M1)

1 − p − q + 5 = 7, 16 + 8p + 2q + 5 = 1 or equivalent      A1A1

attempt to solve their two equations M1

p = −3, q = 2      A1

[5 marks]