Factoring is the process of taking a sum (things added) and rewriting it as a product (things multiplied). We will study several different methods for factoring today. The most basic and most widely applicable is GCF, or Greatest Common Factor, factoring.
This video is good reminder for those who have seen this process before:
If you are really having trouble with finding the GCF, or with the process of factoring out the GCF once you find it, it might help to look at this video — it breaks the process down into more steps, and shows every detail of each step:
The next step is factoring trinomials. Here there are two methods, depending on whether the leading coefficient (the number in front of the x^2 term) is 1, or something else.
Factoring trinomials with a leading coefficient of 1: x^2 + bx + c. The next video is a bit longer (16 minutes) but contains a number of different examples. NOTE: In the video, he uses the letters a and b to refer to the numbers in factored form, NOT the numbers in the original expression.
Factoring trinomial with leading coefficient not 1: ax^2+bx+c. When the leading coefficient is not 1, we use a process called factoring by grouping. NOTE: In the video, he uses the letters a and b to refer to the numbers used in factoring, NOT the numbers in the original expression.
Difference of Squares. Our final factoring rule is based on one of our special products which you may remember from our work on multiplying polynomials,
a^2 – b^2=(a+b)(a-b)