Let's factor the polynomial, first we factor the common factor 6
[tex]6a^2-54=6(a^2-9)[/tex]the term in parenthesis is a difference of square, this can be factor by the rule:
[tex]x^2-y^2=(x+y)(x-y)[/tex]Then we have:
[tex]\begin{gathered} 6a^2-54=6(a^2-9) \\ =6(a+3)(a-3) \end{gathered}[/tex]Therefore the factor polynomial is:
[tex]6(a+3)(a-3)[/tex]