Step-by-step explanation:
Any techniques that you're familiar with can be applied to polynomials of any degree. These might include ...
- use of the rational root theorem
- use of Descartes' rule of signs
- use of any algorithms you're aware of for finding bounds on roots
- graphing
- factoring by grouping
- use of "special forms" (for example, difference of squares, sum and difference of cubes, square of binomials, expansion of n-th powers of binomials)
- guess and check
- making use of turning points
Each root you find can be factored out to reduce the degree of the remaining polynomial factor(s).