Question 2 - A-Level Maths

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Year	2010
Session	June
Topic	Factor & Remainder Theorem
Type	Direct remainder then factorise

2. $$f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } - 58 x + 40$$

Find the remainder when $\mathrm { f } ( x )$ is divided by ( $x - 3$ ). Given that $( x - 5 )$ is a factor of $\mathrm { f } ( x )$,
find all the solutions of $\mathrm { f } ( x ) = 0$.