Set the polynomial equal to zero
Simplify the expression
Factor out any greatest common factor
Use factoring methods if possible
Apply the zero product property
Solve any resulting linear equations
Use substitution for special forms
Use the quadratic formula for degree 2 polynomials
Use synthetic division or long division to reduce higher-degree polynomials
Check for rational roots with the Rational Root Theorem
Use graphing or numerical methods if exact factoring is difficult
Verify all solutions by substituting them back into the original polynomial