Question 1 - A-Level Maths

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Year	2011
Session	June
Topic	Factor & Remainder Theorem
Type	Direct remainder then factorise

1. $$f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } - 5 x + 4$$

Find the remainder when $\mathrm { f } ( x )$ is divided by $( x - 1 )$.
Use the factor theorem to show that ( $x + 1$ ) is a factor of $\mathrm { f } ( x )$.
Factorise f(x) completely.