No, it's not a zero-polynomial.

A monic 7th-degree polynomial would look like this:

.

(You should write polynomials in standard form, ie. with exponents in descending order. I'm changing the coefficients to .)

If P(x) is odd, then P(-x) = -P(x):

In order forP(-x)to equal-P(x),

,

so

.

01