What are the 5 methods of factoring polynomials?
Matthew Wilson
Updated on April 28, 2026
Types of Factoring polynomials
- Greatest Common Factor (GCF)
- Grouping Method.
- Sum or difference in two cubes.
- Difference in two squares method.
- General trinomials.
- Trinomial method.
What is the Trinomial method?
The “AC” Method (Factoring Trinomials) The “AC” method or factoring by grouping is a technique used to factor trinomials. A trinomial is a mathematical expression that consists of three terms (ax² + bx + c).
How do you factor polynomials using GCF?
Factor the greatest common factor from a polynomial
- Find the GCF of all the terms of the polynomial.
- Rewrite each term as a product using the GCF.
- Use the Distributive Property ‘in reverse’ to factor the expression.
- Check by multiplying the factors.
Why does AC method work?
So by multiplying ac in a trinomial, then using the factors of ac whose sum is b, that allows us to rewrite the linear term of the polynomial as a sum of two linear terms. This pattern also works when a = 1 and when factoring the difference of two squares.
What are the three methods of factoring?
Methods of Factoring Common factor. In an expression composed of multiple terms, try to identify if there is one number/variable that is a common factor to each term. Difference of squares. Difference of cubes / Sum of cubes. Grouping. Trial and Error.
How do you write polynomials in factored form?
Writing a polynomial in factored form when given the x-intercepts (zeros) of an equation, and their multiplicity: If a= coefficient, n1= first x-intercept (zero), n2= second x-intercept (zero), etc.
How do I factor each polynomial?
To factor a polynomial completely is to find the factors of least degree that, when multiplied together, make the original polynomial. Stated mathematically, to factor a polynomial P(x), is to find two or more polynomials, say Q(x) and R(x), of lesser degree such that P(x) = Q(x) · R(x).
What are the different kinds of polynomials?
Zero or Constant polynomial
