3.23: Show a linear relation, then find aa, bb, cc

0606/13/O/N/24 — Question 5 · 6 marks

The polynomial pp is such that p(x)=ax3+bx219x+cp(x) = ax^{3} + bx^{2} - 19x + c, where aa, bb and cc are integers. It is given that x+2x + 2 is a factor of p(x)p(x). When p(x)p(x) is divided by x+1x + 1 the remainder is 2020.
(a)
Show that 7a3b=397a - 3b = 39.
[3]
(b)
It is also given that when p(x)p'(x) is divided by x1x - 1 the remainder is 11.
Find the values of aa, bb and cc.
[3]