Consider the polynomial 6x^4+24x^3-72x^2. what is the greatest common factor of the terms of the polynomial

First, look at the coefficients, 6, 24, -72. 6 is a factor of 6, 24, and -72. Since one of the coefficients is in fact 6, then 6 is the GCF of the coefficinets.

Now look at the variables. You have x^4, x^3, and x^2. Remember what the exponents mean. They mean a multiplication of several factors of x.

x^4, x^3, x^2 mean , xxx, xx

, xxx, xx have 2 factors of x in common, so the greatest common factor of the variables is xx which is the same as x^2.

When you put together the common factor of the coefficients and the common factor of the variable parts, you get GCF = 6x^2.