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

Question

Decompose the following expression into factors by removing the common factor:

xyz+yzt+ztw+wtr xyz+yzt+ztw+wtr

Video Solution

Step-by-Step Solution

Factor the given expression:

xyz+yzt+ztw+wtr 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,yzt,ztw,wtr 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.

Answer

It is not possible to decompose the given expression into factors by extracting the common factor.