What is the greatest common factor of the terms in the polynomial 4x4 – 32x3 – 60x2?
4
4x
4x^2
4x^3

The answer is:  4x².   

Explanation:

The polynomial expression given is:

  " 4x⁴ – 32x³ – 60x² "
 By looking at EACH of the 3 (three) terms in the polynomial given:

      4x⁴  , 32x³, and 60x²  , 

We can see that there are only 3 (three) terms; and EACH of the three terms contains a variable "x"; and no other variables that "x".

We also can see that EACH of the 3 (three) terms has an "x" raised to a power of "2" or more; specifically, one term has an "x" raised to a power of "2", the other to a power of three (higher than a "2"); and the other to a power of a "4".  So, we know we can "factor out" an "x² "; and that "x² " will be part of the GCF (greatest common factor) in our equation.  

At this point, we can look at our "answer choices given", realize that only ONE of the answer choice contains and "x² " as part of the answer
[that is, "4x² "]; and that there is no "none of the above" as an answer choice.

However, we can see that among the terms in the polynomial term, the term with the LOWEST coefficient is "4", and the other 2 (two) coefficients are: "32" and "60"; and both "32" and "60" (as well as "4" itself) have "4" as a factor.

This confirms that "4x² " is our answer.


4x² is the greatest common factor (GCF)  of the terms in the polynomial, 
 " 4x⁴ – 32x³ – 60x² " .