Answer:
Step-by-step explanation:
Firstly, I believe that the equation should be represented as [tex]8x^{3} -6x^{2} y^{2} +4x^{2}y[/tex] and [tex]2x^{2} .[/tex] Please correct me if I am wrong and I will fix the equation accordingly.
To find the greatest common factor of this equation, we firstly need to factor the polynomial [tex]8x^{3} -6x^{2} yx^{2} +4x^{2} y[/tex]. To do this:
1. Find a GCF for all of the coefficients of the equation. To do this, you can make factor trees, or you can simply just use the prime factorization method.
The prime factorization method is simply a technique used to list the prime numbers used to find the total value. For example, what two prime numbers do you multiply to get four? 2 and 2. 2 is a prime number.
The prime factorization for each of the coefficients is as follows.
8: 2³
6: 2 · 3
4: 2²
We have 2s as values in every prime factorization, but we only one of each. We must take the greatest common value, and 2 is this value. So, our GCF coefficient is 2.
Now, we look at our x variables and y variables.
For x, we have x³ and x². So, our GCF is x².
Our GCF is now 2x². Now, let's look at our y-variables.
We don't have y variables for our entire polynomial, so it can't be a common factor. Therefore, our GCF is 2x².
