Let's break apart each term into its factors:
[tex]\begin{gathered} 14a^3=2\cdot7\cdot a\cdot a\cdot a \\ 35a^2=5\cdot7\cdot a\cdot a \\ 42a=2\cdot3\cdot7\cdot a \end{gathered}[/tex]The common factors are
7 * a
That is,
[tex]7\cdot a=7a[/tex]Now, factorizing the expression, we have:
[tex]\begin{gathered} 14a^3+35a^2+42a \\ =7a(2a^2+5a+6) \end{gathered}[/tex]Answer[tex]7a(2a^2+5a+6)[/tex]