Why is the gcf important in factoring polynomials

You can check this by doing the multiplication. Note that if you do not factor the greatest common factor at first, you can continue factoring, rather than start all over. Notice that you arrive at the same simplified form whether you factor out the GCF immediately or if you pull out factors individually. In the following video, we show two more examples of how to find and factor the GCF from binomials.

We will show one last example of finding the GCF of a polynomial with several terms and two variables. No matter how large the polynomial, you can use the same technique described below to factor out its GCF. First, find the GCF of the expression.

Next, determine what the GCF needs to be multiplied by to obtain each term of the polynomial. Finally, write the factored expression as the product of the GCF and the sum of the terms we needed to multiply by. After factoring, we can check our work by multiplying.

In the following video, you will see two more example of how to find and factor our the greatest common factor of a polynomial. Skip to main content. You will need to divide monomials in order to factor polynomials. Not too hard, is it? Same process, you just have to be careful to look at all the variables.

You must be able to factor out of every term in order to identify the GCF. Hopefully you now understand how to factor polynomials if the polynomials have a greatest common factor. Remember, all polynomial problems will not have a GCF, and we will discover in the next few lessons how to factor if there is no GCF.

The next lesson is on factoring by using grouping. Click here for more information on our affordable subscription options. Not ready to subscribe?

Click here for more information on our Algebra Class e-courses. For instance, you could start with the polynomial and work backwards to. To do this, first identify the GCF of a polynomial. Look at finding the GCF of several numbers. To find the GCF of several numbers, look for the largest number that each of the numbers can be divided by. Find the GCF of , , and. First, break all these numbers into their primes.