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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 24, 2024
 #1
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I would show all the steps to the problem, but that would be a bit time consuming, so I will highlight the way to go. 

 

We just have to use the distributive property to get \({x^{3}\left(x^{4}-8x^{3}+17x^{2}-23x+14\right)+x^{2}\left(x^{4}-8x^{3}+17x^{2}-23x+14\right)+x\left(x^{4}-8x^{3}+17x^{2}-23x+14\right)+1\left(x^{4}-8x^{3}+17x^{2}-23x+14\right)}\)

 

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

 

So the coefficient of x is -9. 

 

Thanks! :)

 May 24, 2024

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