2.11: Factor and remainder on a cubic (Paper 23)

0606/23/M/J/18 — Question 4 · 6 marks

Do not use a calculator in this question.

It is given that x+4x + 4 is a factor of p(x)=2x3+3x2+ax−12p(x) = 2x^{3} + 3x^{2} + ax - 12. When p(x)p(x) is divided by x−1x - 1 the remainder is bb.
(i)
Show that a=−23a = -23 and find the value of the constant bb.
[2]
(ii)
Factorise p(x)p(x) completely and hence state all the solutions of p(x)=0p(x) = 0.
[4]