Question

Factorise the following:
2^(n+1)+3(2^n)+2^(n-1)

Answer 1

\[2^{n+1}=2(2^n)\]\[2^{n-1}=2^{-1}2^n=\frac{1}{2}(2^n)\]now u have\[2(2^n)+3(2^n)+\frac{1}{2}(2^n)\]now factor out 2^n\[=2^n(2+3+\frac{1}{2})=\frac{11}{2}(2^n)\]

Answer 2

\[
\frac {11} 2 2^n= 11\, \,( 2^{n-1})
\]