Question 4 - A-Level Maths

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Year	2006
Session	June
Topic	Factor & Remainder Theorem
Type	Direct remainder then factorise

$$f ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 29 x - 60$$

Find the remainder when $\mathrm { f } ( x )$ is divided by $( x + 2 )$.
Use the factor theorem to show that $( x + 3 )$ is a factor of $\mathrm { f } ( x )$.
Factorise $\mathrm { f } ( x )$ completely.