Find the Coefficient of x17 in a Tricky Polynomial Product

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Discussion Overview

The discussion centers around finding the coefficient of x17 in a specific polynomial product without factoring or using multinomial theorems. The scope includes mathematical reasoning and exploration of polynomial properties.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the coefficient of x17 might be 0.
  • Another participant agrees, stating that it is indeed 0.
  • A further participant confirms the previous claims, asserting that it can be proven using properties of even and odd functions.

Areas of Agreement / Disagreement

Participants generally agree that the coefficient of x17 is 0, with multiple confirmations of this viewpoint.

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

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