B is no because if the degree of the denominator is not 1 then you cannot use synthetic divisison.

C it can be used its just a little more challenging

A the last row is the remainder and when dividing polynomials you can get a remainder which means it is not always 0

This leaves D which is the right answer

this is the site i use: http://www.math.psu.edu/files/Section%204.4%20class%20notes%20New.pdf

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