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How to Factor Polynomials: Follow this free, step-by-step guide on how to factor polynomials include binomials, trinomials when the leading coefficient is one and when the leading coefficient is not one, factoring by completing the square, and factoring by grouping.
Learn how to factor polynomials with 2, 3, 4, or more terms with rules, methods, steps, examples, and diagrams.
Let's discuss the methods of factoring polynomials, and some of the important concepts related to factoring polynomials: remainder theorem, factor theorem, GCF, long division.
Factoring polynomials is done in pretty much the same manner. We determine all the terms that were multiplied together to get the given polynomial. We then try to factor each of the terms we found in the first step. This continues until we simply can’t factor anymore.
In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of computer algebra systems.
For polynomials with four or more terms, regroup, factor each group, and then find a pattern as in steps 1 through 3. For all polynomials, first factor out the greatest common factor (GCF). For a binomial, check to see if it is any of the following: difference of squares:
You have now become acquainted with all the methods of factoring that you will need in this course. (In your next algebra course, more methods will be added to your repertoire.)