Question 6 - A-Level Maths

Exam Board	OCR MEI
Module	C1 (Core Mathematics 1)
Year	2010
Session	June
Topic	Factor & Remainder Theorem
Type	Find constants from coefficient conditions

6 You are given that

the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( 5 + 2 x ^ { 2 } \right) \left( x ^ { 3 } + k x + m \right)\) is 29 ,
when \(x ^ { 3 } + k x + m\) is divided by ( \(x - 3\) ), the remainder is 59 .

Find the values of \(k\) and \(m\).