what is the greatest common factor of the polynomial show?
rectangle tiles that have 6x and 6 look like this:
** ** ** ** ** **
** ** ** ** ** **
** ** ** ** ** **
** ** ** ** ** **
!!! !!! !!! !!! !!! !!!
To find the greatest common factor of a polynomial, we need to factorize the polynomial into its prime factors and determine the highest power shared by each factor.
In this case, we have a visual representation of rectangle tiles, which consist of groups of "6x" and "6". To find the greatest common factor, we need to determine the highest power that appears in all the terms.
Looking at the rectangle tiles, we can see that both "6x" and "6" appear together in each row and column. We can represent this visually as:
6x * ** ** ** ** **
6 * ** ** ** ** **
6 * ** ** ** ** **
6 * ** ** ** ** **
6 * ** ** ** ** **
6 * ** ** ** ** **
Now, let's consider the prime factorization of each term:
6x = 2 * 3 * x
6 = 2 * 3
From this, we can identify that the greatest common factor shared by "6x" and "6" is 2 * 3, which is equal to 6. Therefore, the greatest common factor of the polynomial is 6.
Using this process, you can find the greatest common factor of any given polynomial or set of terms.