A linear factor is a factor of degree 1. In other words, it can be written in the form, where and are constants and is not equal to . For the quadratic polynomial , the linear factors are and .
The greatest common factor, or GCF, of two or more numbers is the largest positive integer that divides evenly into all of the numbers (i.e. leaves a remainder of 0). For example, the GCF of 60 and 18 is 6.
The GCF of two or more polynomials is the largest polynomial of the highest degree that can be factored out of all of the polynomials in question. For example, the GCF of and is .
When we have a difference of two squares, likeor , the expression can be factored according to a certain pattern. In general, . For the two examples already mentioned, then, we could factor to have and .
Factoring by grouping is a technique that can be used to factor certain polynomials that can be written with more than 3 terms. Let’s look at a couple of examples:If we start out with a polynomial that only has three terms, we can often expand the middle term and then factor by grouping.
Polynomials that are simply sums or differences of cubes factor according to particular patterns.
For any expression of the form , we can say that For any expression of the form , we can say that