How to divide a polynomial into two polynomials, one with the odd coefficients of w and the other with the even coefficients of w?

I have the polynomial p(w) described below and I need to split it into two polynomials one with odd coefficients of w and the other with even coefficients of w, how can I do that?

P(w) = 25*ki - w^4*(kd + 1) + w*(25*kp - 1)*1i + w^3*(kp + 33/5)*1i + w^2*(ki - 25*kd + 41/5)

[Jan]

How could the readers decide, if e.g. (25*kp - 1)*1i is even or odd?

[Torsten]

Not necessary - the polynomial is in w, not kp.

[Alex Muniz]

kp is a constant. The polynomial is a function of w.

I would like two polynomials as follows:

P(w) = 25*ki - w^4*(kd + 1) + w*(25*kp - 1)*1i + w^3*(kp + 33/5)*1i + w^2*( ki - 25*kd + 41/5)

P(w) = P_odd(w) + P_even(w)

P_odd(w) = w^3*(kp + 33/5)*1i + w*(25*kp - 1)*1i

P_even(w) = -w^4*(kd + 1) + w^2*( ki - 25*kd + 41/5) + 25*ki

Answer 1

[Torsten]

Odd part:

(P(w) - P(-w))/2

Even part:

(P(w) + P(-w))/2

syms w kd ki kp
P(w) = 25*ki - w^4*(kd + 1) + w*(25*kp - 1)*1i + w^3*(kp + 33/5)*1i + w^2*( ki - 25*kd + 41/5);
P_odd(w) = (P(w)-P(-w))/2

P_odd(w) = 

P_even(w) = (P(w) + P(-w))/2

P_even(w) = 

P_odd(w) + P_even(w) - P(w)

ans = 

0

[Jan]

Now the question is getting clearer to me.