[knaik94]

Given the first polynomial, when asked to solve it, there's an implied "for x" attached to the question. Even in higher level math you assume you're solving for a variable. When writing an equation without a solution, you don't naturally think about not including any variables. While 0 = 1 is an equation, it's not an equation you "solve". The meaning of equation is not in question, just the association of the terminology of equation to something without variables. Context is important, if the expression had a third order term and I had to use synthetic division, I would absolutely write include the zero terms.