Question 1 - A-Level Maths

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2016
Session	March
Topic	Binomial Theorem (positive integer n)
Type	Coefficient zero after multiplying binomial

Find the coefficients of \(x ^ { 4 }\) and \(x ^ { 5 }\) in the expansion of \(( 1 - 2 x ) ^ { 5 }\).
It is given that, when \(( 1 + p x ) ( 1 - 2 x ) ^ { 5 }\) is expanded, there is no term in \(x ^ { 5 }\). Find the value of the constant \(p\).