Find the Coefficient of x17 in a Tricky Polynomial Product

[Char. Limit]

Quick! Without factoring or using any multinomial theorems, give me the coefficient of x¹⁷ in the polynomial product:

(x³+23x)(x⁶+35x⁴+1685)(x¹⁹+1246x⁹)

Can you do it?

 

[micromass]

Is it 0?

 

[ARAVIND113122]

it is 0.

 

[Char. Limit]

Yes, it is 0, as can be proven using just the properties of even and odd functions.