The given expression is
[tex]4x^3+24x+x^2+6[/tex]Let's group them as follows
[tex](4x^3+x^2)+(24x+6)[/tex]In the first group, we can factor out the greatest common factor x2. In the second group, we can factor out 6.
[tex]x^2(4x+1)+6(4x+1)[/tex]As you can observe, we have a common factor, let's factor it out
[tex](4x+1)(x^2+6)[/tex]