Factoring Polynomials
Factoring polynomials can be a very simple and easy process, but it is often seen as a very daunting task to students. There are several different method used to factor polynomials. Some of the easier techniques include factoring by the greatest common factor (GCF) and grouping. Both methods work well with most equations, there are the exceptions where a quicker technique is easier, like when you would use the sum of cubes, difference of cubes, and even the difference of squares.
The concept of using the GCF relies on there being at least one shared factor in all terms of the polynomial. That shared factor, or if present factors, is/are the greatest common factor. We divide out the GCF and the remainder is left inside the polynomial. Sometimes factoring out the GCF may be as far as you can factor, but there are many times where the remainder can still be factored using the grouping method. |
The grouping method allows for terms that have a common factor to be grouped together in parentheses. This makes it possible for the remainders to be factored again using a GCF. Normally the two factors that come out of the separate groups are added or subtracted together in their own set of parentheses.
Another technique that I included examples for is the reverse FOIL method. This method can take a trinomial and factor it into two separate binomials. The first values in the binomials must multiply to equal the first value in the trinomial. The last values must multiply to be the last value in the trinomial. When you multiply the outer and then the inner binomial value, they need to be able to add together to equal the middle term in the trinomial. This method is used very often, but can sometime trip students up when it comes to making sure all of the signs match. Knowing how your negative and positive value combine when using multiplication, addition, and subtraction is crucial with this method. |