Answer:(x-2)(x-3)(x-4)
Explanation:
Use the rational root theorem to get started, then factor the remaining quadratic to find:
f(x)=x^3-5x^2-2x+24
f(2)=(2)^3-5(2)^2-2(2)+24
f(2)=0
i.e 2 is a root of f(x)
(x-2) is a factor
Now by dividing x^3-5x^2-2x+24by (x-2),
we get q(x)=x^2-7x+12
Since, q(x) is also a factor of x^3-5x^2-2x+24
Factorising x^2-7x+12
(x-4)(x-3)
So, all the factors of
x^3-5x^2-2x+24 are (x-4),(x-3) and (x-2)