Pls Help (Polynomial Factor Question)

I'd start by considering factors of 24    

plus or minus  1,2,3,4,6,8,12,24     That's a lot  16 in total

Now trial and error to see which one will divide in perfectly.

 

\(f(x)=x⁴-2x³-13x²+38x-24\\ f(1)=1-2-13+38-24 =39-39=0\;\;great\\ (x-1)\text{ is a factor} \)

 

Now I would divide f(x) by  x-1    to get the dividend then start the process again.

OR you could just look for another possibility out of the list.