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

 Jun 30, 2024
 #1
avatar+1250 
+1

To solve this problem, let's focus on the ways we can get x in the problem. 

First, we have x and 14. 

We get \(14x\) from this. 

Next, we have 1 and \(-23x\)

Multiplying these two together, we get

\(-23x\)

 

Adding these two together, we get \(14x-23x=-9x\)

 

We could also expand everything out. Using the Distributive Property, we get

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

 

Thus, the coefficient is -9. 

 

So our answer is -9. 

 

Thanks! :)

 Jun 30, 2024

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