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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 4, 2023
 #1
avatar+222 
-1

We expand the given polynomial and then combine like terms.

 

[ \begin{array}{r r c r@{}l} &x^3 + x^2 + x + 1 & (x^4 - 8x^3 + 17x^2 - 23x + 14)

 

& \ \times\phantom{=} & x^4 & x^7 & - 8x^6 & +17x^5 & - 23x^4 & +14x^3 & -8x^2 & + 4x & - 14\ &

 

+x^2 & x^6 & - 8x^5 & +17x^4 & - 23x^3 & +14x^2 & -8x+ 4x & -14\ & +x & x^5 & -8x^4 & +17x^3 &

 

- 23x^2 & +14x& -8x& +4x & -14\ & +1 & x^4 & - 8x^3 &+ 17x^2 & - 23x & + 14 & - 8x & +4x & - 14\

 

\cline{2-10} & x^7 & - 3x^6 & +14x^5 & +18x^4 & - 5x^3 & +3x^2 & -14x & -18 & \end{array} ]

 

Therefore, the coefficient of x is −14​.

 Dec 4, 2023

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