The greatest common factor of the monomials is [tex] 2x^{2} [/tex].
To start by finding this, we need to find the largest number that goes into all coefficients evenly. We'll start with the factors of 6, which are 1, 2, 3, and 6. Neither 3 nor 6 does goes into 8 evenly. 2 goes into each of the other two terms, so we use that as the coefficient.
Next we take the term with the smallest number of x's and we take all of those from all. Since the middle term has 2 x's and each of the others have at least that many, that's what we take out when we factor.
