2.2: Remainder and complete factorisation

0606/21/M/J/20 — Question 3 · 6 marks

Do not use a calculator in this question.

The polynomial p(x)=15x3+22x2−15x+2p(x) = 15x^{3} + 22x^{2} - 15x + 2.
(a)
Find the remainder when p(x)p(x) is divided by x+1x + 1.
[2]
(b)(i)
Show that x+2x + 2 is a factor of p(x)p(x).
[1]
(b)(ii)
Write p(x)p(x) as a product of linear factors.
[3]