what is the greatest common factor of the polynomial show:
rectangle tiles that have 6x and 6 look like this:
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To find the greatest common factor of the given polynomial, we need to identify the common factors shared by all terms and determine the highest power of each factor that they have in common.
In this case, the polynomial has terms represented by rectangle tiles with dimensions 6x and 6. The greatest common factor is obtained by determining the common factors of the length (6) and the variable (x) between all the terms.
The common factor for the length is 6, and for the variable, it is x. To find the highest power of each factor, we count the number of tiles that have 6 (length) and x (variable) respectively.
From the visual representation:
Length (6): There are 5 columns with 6 tiles each, so the highest power of 6 is 5.
Variable (x): There are no tiles with an x, so the highest power of x is 0.
Therefore, the greatest common factor of the polynomial is 6^5 or 7776.