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What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)?

 Jan 7, 2025
 #1
avatar+1946 
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There are a few ways you can tackle this problem. 

The first way is reccomended. We find that after distributing, how many pairs create a coefficient of x. 

 

We first have x and 14. 14x=14x

Next, we have 1 and -23x. 123=23x

 

These are the only two ways to achieve x. Now, we simply add then up. 

14x23x=9x

 

Orrrrrrrrrrrrrrrrrrrrrrrrrrr, you can distribibute EVERYTHIG and take 100 years, but here u go :)

x77x6+10x513x4+8x29x+14

 

Thanks! :)

 Jan 7, 2025
edited by NotThatSmart  Jan 7, 2025

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