How do I find the greatest common factor of a polynomial? When finding the greatest common factor of a polynomial, can it ever be larger than the smallest coefficient and can it ever be smaller than the smallest coefficient? Please explain.

Since this is not my area of expertise, I searched Google under the key words "math gcf" to get these possible sources:

http://www.google.com/search?client=safari&rls=en&q=math+gcf&ie=UTF-8&oe=UTF-8

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.

can someone help me

To find the greatest common factor (GCF) of a polynomial, you need to factor each term of the polynomial and identify the highest power of each variable that appears in all terms. The GCF is the product of these common factors.

Here's a step-by-step process to find the GCF of a polynomial:
1. Identify the terms of the polynomial.
2. Factor each term completely. For example, if you have the term 8x^3, it can be factored as 2 * 2 * 2 * x * x * x.
3. Identify the highest power of each variable that appears in all terms. For example, if you have the terms 8x^3 and 12x^2, the highest power of x that appears in both terms is x^2.
4. Find the product of all the common factors identified in step 3. In the above example, the GCF would be 2 * 2 * x^2 = 4x^2.

Now, let's address your specific questions. The GCF of a polynomial can never be larger than the smallest coefficient. This is because the GCF is a factor that appears in all terms, and it would mean that there is a common factor that is larger than the smallest coefficient.

On the other hand, the GCF of a polynomial can be smaller than the smallest coefficient. This is because the GCF only considers the factors that appear in all terms, irrespective of their individual magnitudes. So, it's possible for the GCF to be a smaller factor when compared to the coefficients of certain terms in the polynomial.