$p\;(x)=\large\frac{1+x^2+x^4+\;...\;x^{2n-2}}{1+x+x^2+\;...\;+x^{n-1}}\;$ is a polynomial in x , then n must be

Question

$(a)\;even \qquad(b)\;even\qquad(c)\;odd\;than\;10\qquad(d)\;greater\;than\;10$