3.25: Cubic with factor and remainder

0606/12/O/N/25 — Question 2 · 7 marks

The polynomial pp is such that p(x)=2x3+ax2+13x+bp(x) = 2x^{3} + ax^{2} + 13x + b, where aa and bb 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 there is a remainder of 66.
(a)
Find the values of aa and bb.
[4]
(b)
Show that the equation p(x)=0p(x) = 0 has only one real root.
[3]