# How is the degree of a polynomial defined? $a_1+a_2x^2+\cdots+a_nx^{n-1}$ has degree $n$ or $n-1$?

I have this polynomial: $$a_1+a_2x^2+\cdots+a_nx^{n-1}$$ or: $$a_0+a_1x^2+\cdots+a_{n-1}x^{n-1}$$ What is degree of those polynomials? $n$ or $n-1$, I'm little bit confuse...

Thank you!

• The degree is the largest exponent of $x$ in the polynomial which here is $n-1$ in both cases. – Winther May 26 '15 at 19:53
• More precisely, it is $n-1$ if the coefficient of $x^{n-1}$ is nonzero. – Robert Israel May 26 '15 at 20:08

It's $n-1$ in both cases. But we choose the pointers to the coefficients to be the same with the degree of each monomial.