What is the coefficient of x in (x3+x2+x+1)(x4−8x3+17x2−23x+14)?
Out of the entire equation (which is quite messy), we only need to pay attention to the x term. There are two possible ways to get a term that has degree one in this equation: 1⋅−23x and x⋅14. Therefore, the coefficient of x is the sum of those two terms, which is −9x.
Feel free to correct me if I'm wrong! :D