Question 964570
Rational Roots Theorem and synthetic division.  The roots to check would be -1, -2, -4,- 5, -10, maybe -20.


You asked for a first step.  Take as example 5;  is  {{{x+5}}} one of the binomial factors of the cubic polynomial?  Check the root  -5 using synthetic division.



__________-5_______|_________1______5_______4_______20
__________________|
__________________|_______________-5________0______-20
___________________________________________________________
____________________________1______0______4_________0


Remainder is 0, so this means -5 is a root, or equivalently,  (x+5) is one of the binomial factors of the polynomial given.


The quotient from the synthetic division shows  the other factor is  {{{x^2+4}}}.  This will have two complex roots.