Factor the Expression: Decomposing xyz+yzt+ztw+wtr Using Common Factors

Factor the given expression:

$xyz+yzt+ztw+wtr$
We will do this by extracting the highest common factor, both from the numbers and the letters.

We refer to the numbers and letters separately, remembering that a common factor is a factor (multiplier) common to all terms of the expression.

As the given expression does not have numeric coefficients (other than 1), we will look for the highest common factor of the letters:

There are four terms in the expression:
$xyz,\hspace{4pt}yzt,\hspace{4pt}ztw,\hspace{4pt}wtr$We will notice that in each of the four members there are three different letters, but there is not one or more letters that are included (in the multiplication) in all the terms; that is, there is no common factor for the four terms and therefore it is not possible to factor this expression by extracting a common factor.

Therefore, the correct answer is option d.