Mathematics

Problem

Consider the polynomial

s(x)=2x^4+px^3+qx^2+8x+4

where

p

and

q

are integers. The polynomial is exactly divisible by

(x-2)

. a. (i) Derive the relation between

p

and

q

that follows from the given condition. b. (ii) Find all ordered pairs

(p, q)

satisfying the relation obtained in part (i) if

0\le p\le10