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

 Dec 3, 2024
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Every item in the first term is multiplied with every item in the second term. 

Pick out the items that, when multiplied, result in an "x" coefficient product.  

 

(x3 + x2 + x + 1) • (x4 – 8x3 + 17x2 – 23x + 14)     gives you + 14x    

(x3 + x2 + x + 1) • (x4 – 8x3 + 17x223x + 14)     gives you 23x    

 

add them together for the final value                                     9x    

.    

 Dec 3, 2024
edited by Bosco  Dec 3, 2024

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