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

Rangcr897 Jul 7, 2024

#1**+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! :)

NotThatSmart Jul 8, 2024