Factor polynomials by identifying the greatest common factor and by grouping four-term polynomials.
Factoring is multiplying in reverse: instead of distributing a factor across a sum, you find what every term already has in common and pull it back out. The greatest common factor (GCF) of a polynomial is the largest monomial that divides every single term - find the GCF of the coefficients (regular number GCF) and the smallest matching power of any shared variable, then write the polynomial as GCF times what is left over.
A four-term polynomial often factors by grouping: split it into two pairs, pull the GCF out of each pair separately, and if both pairs leave behind the SAME binomial, that matching binomial is itself a common factor you can pull out one more time. Always check a factoring answer by multiplying it back out - if you do not land exactly back on the original polynomial, something slipped.
Mastery looks like: They find the correct GCF (numeric and variable) and factor a four-term polynomial by grouping, checking by re-multiplying.
Common stumbles: Pulling out a partial GCF and stopping early (e.g., 2x²(4x+6) instead of 4x²(2x+3)); forgetting to also factor out a shared binomial after grouping.