Algebra guide
Factoring Polynomials Step by Step
Factor out the GCF, recognize standard identities, and break quadratic trinomials into linear factors.
8 min readBeginnerUpdated 2026-07-12
What you will learn
- Extract the greatest common factor
- Recognize a difference of squares
- Factor monic quadratic trinomials
Concept 1
Always check for a common factor first
The greatest common factor includes both the numerical GCF and every variable power shared by all terms.
Concept 2
Learn the standard identities
A difference of squares factors into conjugates. Perfect-square trinomials come from squaring a binomial.
Concept 3
For x²+bx+c, search by product and sum
Find numbers m and n with mn=c and m+n=b. Then the factors are (x+m)(x+n).
Worked example
Factor x²−5x+6
- 1The GCF is 1.
- 2Find factors of 6 whose sum is −5: −2 and −3.
- 3Write the corresponding binomial factors.
Answer
Common mistakes
- Skipping the greatest common factor
- Forgetting that signs must match both the product and the sum
- Stopping before checking whether factors can be factored again
Check your understanding