Question

GIVING MANY POINTS!
Let p=x^999 − x^100+3x^9 − 5 and q=x + 1. Since q has degree 1, it follows that the remainder when p is divided by q is a constant function k, for some k. What is the value of k?

Answer 1

The polynomial remainder theorem gives an immediate answer. It says that the remainder upon dividing $p(x)$ by $x-c$ is exactly $p(c)$. In this case $q=x+1\implies c=-1$, and we have

$k=p(-1)=(-1)^{999}-(-1)^{100}+3(-1)^9-5=-1-1-3-5=-10$

Answer 2

Answer:

The polynomial remainder theorem gives an immediate answer. It says that the remainder upon dividing  by  is exactly . In this case , and we have

Step-by-step explanation: