The polynomial given is `15x^2 - 12x`. To find the common factor, we need to analyze both the coefficients and the variables separately.
1. Coefficients: The coefficients in the given polynomial are 15 and 12. The common factor between 15 and 12 is 3, determined by finding the largest number that divides both 15 and 12 evenly.
2. Variables: The variables in the given polynomial are x^2 and x. When we find the variable factor, we should consider the powers of variables. The power of `x` in `x^2` is 2 and in `x` is 1. Thus, the common factor between x^2 and x is x.
Finally, by combining the common coefficient factor and the common variable factor, we get the common factor for the polynomial. So, the common factor of 15x^2 - 12x is 3x.