+864 What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?
+1804 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! :)
