Because (x-a)(x-b)(x-c) will be 0 at the values ie a,b,c so remainder at each of these values will be p(a),p(b),p(c) ie a,b,c. So, eg if we take a we get pa^2 + qa + r = a , ie pa^2 +a(q-1) + r = 0 . In all a,b,c we get same expression. So I think that means a , b ,c will be roots of px^2 +...