1. Check for common factors. If the terms have common factors, then factor out the greatest common factor (GCF) and look for the resulting polynomial factors to factor further.
2. Determine the number of terms in the polynomial:
- Four term polynomials are factored by grouping.
- Trinomials (3 terms) are factored using “trial and error” or the AC method.
- Binomials (2 terms) are factored using the following special products.
3. Look for factors that can be factored further.
4. Check by multiplying.
* If a binomial is both difference of squares and cubes, then we should factor it as difference of squares first to obtain a more complete factorization.
* Not all polynomials with integer coefficients factor, in this case, we say that the polynomial is prime.
Solution: This four term polynomial has a GCF of 3x , we factor this out first.
You can check by multiplying. A similar problem can be found on YouTube:
You will find many more embedded videos in the Elementary Algebra textbook, here are links to the appropriate sections:
6.1 Introduction to Factoring
6.2 Factoring Trinomials x^2 + bx + c
6.3 Factoring Trinomials ax^2 + bx + c
6.4 Factoring Binomials
6.5 General Guidelines for Factoring Polynomials
Learning how to factor takes lots of time and practice.
