Question 1129675

{{{(2n+1)(n+5) -2(n+3) - (5n+13)}}}

Hint: an integer is divisible by {{{6 }}}if and only if it is divisible by both {{{2}}} and {{{3}}}. 

Can you show that your expression is even,divisible by both {{{2}}} and {{{3}}} ? 

first simplify it:

{{{(2n+1)(n+5) -2(n+3) - (5n+13)}}}

{{{2n^2+10n+n+5 -2n -6 - 5n-13}}}

{{{2n^2+11n +5 -7n -6 -13}}}

{{{2n^2 +4n+5-19}}}

{{{2 n^2 + 4 n - 14}}}

{{{2 (n^2 + 2 n - 7)}}} => GFC is {{{2}}}; 

so,it is divisible by {{{2}}}, 

but it is {{{not}}} divisible by {{{3}}}

=>consequently, it is {{{not}}} divisible by {{{6}}} either