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

 May 28, 2024

Best Answer 

 #1
avatar+1280 
+1

I'm going to do this the hard way and expand eveyrhing out. 

 

Expanding the awful polynomial, which I DEFINTELY NOT reccomending, we have

\(x^{7}-7x^{6}+10x^{5}-13x^{4}+8x^{2}-9x+14\)

 

As you can seem the coefficient is just -9. 

 

If you want to simplify the process, just note this. 

In the expansion, the only two terms that matters is 1*-23x amd x*14x. Adding these 2 we get -9. 

 

Thanks! :) 

 May 28, 2024
 #1
avatar+1280 
+1
Best Answer

I'm going to do this the hard way and expand eveyrhing out. 

 

Expanding the awful polynomial, which I DEFINTELY NOT reccomending, we have

\(x^{7}-7x^{6}+10x^{5}-13x^{4}+8x^{2}-9x+14\)

 

As you can seem the coefficient is just -9. 

 

If you want to simplify the process, just note this. 

In the expansion, the only two terms that matters is 1*-23x amd x*14x. Adding these 2 we get -9. 

 

Thanks! :) 

NotThatSmart May 28, 2024

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