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−24f(1)=1−2−13+38−24=39−39=0great(x−1) 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.