1.11: Factor and value conditions on a cubic

0606/12/O/N/20 — Question 10 · 8 marks

The polynomial p(x)=6x3+ax2+bx+2p(x) = 6x^{3} + ax^{2} + bx + 2, where aa and bb are integers, has a factor of x−2x - 2. Given that p(1)=−2p(0)p(1) = -2p(0),
(a)
find the value of aa and of bb.
[4]
(b)(i)
find the remainder when p(x)p(x) is divided by 2x−12x - 1,
[2]
(b)(ii)
factorise p(x)p(x).
[2]