If (p(x)=0\cdot x+0), is it a linear polynomial?

Correct answer: No it is the zero polynomial

The direct answer is option C: no, it is the zero polynomial. Since 0·x=0 and the constant term is also 0, p(x)=0·x+0 is simply p(x)=0. A linear polynomial must have degree exactly 1, usually written as ax+b with a≠0. Here the coefficient of x is 0, so there is no actual x term. The zero polynomial is special: its degree is not defined in the usual school convention, so it cannot be called linear. Option A is wrong because merely writing x does not make a term non-zero. Option B is wrong because the degree is not 1; the whole polynomial is zero. Option C is correct because the expression is the zero polynomial. Option D is wrong because a zero constant does not create a linear term. Do not confuse the form ax+b with the condition a≠0. Exam cue: if every coefficient is zero, identify the zero polynomial first; never assign it degree 1.