+769 What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?
+1926 To solve this problem, let's focus on the ways we can get x in the problem.
First, we have x and 14.
We get \(14x\) from this.
Next, we have 1 and \(-23x\)
Multiplying these two together, we get
\(-23x\)
Adding these two together, we get \(14x-23x=-9x\)
We could also expand everything out. Using the Distributive Property, we get
\(x^{7}-7x^{6}+10x^{5}-13x^{4}+8x^{2}-9x+14\)
Thus, the coefficient is -9.
So our answer is -9.
Thanks! :)
