Question 2 - A-Level Maths

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Year	2007
Session	June
Topic	Factor & Remainder Theorem
Type	Direct remainder then factorise

$$f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 16 x + 12$$

Find the remainder when $\mathrm { f } ( x )$ is divided by ( $x - 2$ ). Given that $( x + 2 )$ is a factor of $\mathrm { f } ( x )$,
factorise $\mathrm { f } ( x )$ completely.