What is the coefficient of x in (x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)?
There are a few ways you can tackle this problem.
The first way is reccomended. We find that after distributing, how many pairs create a coefficient of x.
We first have x and 14. 14⋅x=14x
Next, we have 1 and -23x. 1⋅−23=−23x
These are the only two ways to achieve x. Now, we simply add then up.
14x−23x=−9x
Orrrrrrrrrrrrrrrrrrrrrrrrrrr, you can distribibute EVERYTHIG and take 100 years, but here u go :)
x7−7x6+10x5−13x4+8x2−9x+14
Thanks! :)