Set the polynomial equal to zero
Factor out any greatest common factor
Look for special factoring patterns
Use the Rational Root Theorem to test possible rational zeros
Use synthetic division or long division to reduce the polynomial after finding a zero
Continue factoring the remaining polynomial
Solve each factor by setting it equal to zero
Use the quadratic formula if a quadratic factor cannot be factored easily
Check for repeated zeros from repeated factors
Verify all solutions by substituting them back into the original polynomial