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

 Jul 7, 2024
 #1
avatar+1256 
+1

Now, there are two ways to do this problem. 

First off, let's look at the possibilities of how we can create x. 

We have x and 14, which gets us 14x. 

Next, we have -23x and 1, which gives us -23x. 

 

Thus, the coefficient is simply \(14x-23x = -9x\)

 

We could also just expand the entire thing. We find that after expanding out the entire thing, we have

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

 

Thus, the coefficient of x is just \(-9\)

 

So -9 is our answer. 

 

Thanks! :)

 Jul 8, 2024

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