An odd polynomial is an odd degree polynomial but not vice versa. How about a completely odd degree polynomial? I mean how about a polynomial whose terms are odd degree like x^5 + x^3 + x?
Is it an odd polynomial for sure?
Please, explain me

Question

An odd polynomial is an odd degree polynomial but not vice versa. How about a completely odd degree polynomial? I mean how about a polynomial whose terms are odd degree like x^5 + x^3 + x? 
Is it an odd polynomial for sure?
Please, explain me

loser66 · Answer

@mathmale

mathmale · Answer

Hello, Winner66!
If all the exponents of x in the polynomial in question are odd, then I think you can safely label it as an odd polynomial.  

Are  you familiar with the following characteristic of an odd poly.?  f(-x) = -f(x).

In what context did you find this problem?

loser66 · Answer

Yes, I am familiar with odd poly definition
My problem come from my test which I failed when confusing between odd poly and odd degree poly. 
My problem on test was: Let U $\subset P_4$ be the subspace of all polynomials x $\in P_4$ such that x'(0)=0. Let W$\subset P_4$ be the subspace of all odd polynomials.
a) What is U+W? justify your answer
b)What is U$\bigcap$W? justify your answer
c) Write the polynomial x = 1+ t=t^2 +t^3 as a sum of u + w where u $\in U $ and w $\in W$ in 2 different ways.
I failed. hihihihi...

loser66 · Answer

for c * 1+ t+t^2 + t^3

mathmale · Answer

An odd polynomial is one whose every power of x is an ODD integer.

An odd-order polynomial is one whose FIRST TERM involves an ODD power of x.

loser66 · Answer

Got it, thank you so much.

mathmale · Answer

I'm really happy to have been able to help with this.  All the best to you.

loser66 · Answer

Thank you :)