There is a given polynomial: $p(x)=(x^n-x+1)^{2018}(3x^{n+3}+2x-4)^{11}$

Question

$$p(x)=(x^n-x+1)^{2018}(3x^{n+3}+2x-4)^{11}$$

1. What is the remainder if you divide this polynomial with $g(x)=x-1$
2. What should $n$ be that the degree of the polynomial is $4091$
3. Calculate the sum of all the coefficients of polynomial $p(x)$

Answer 1

(a)for finding remainder when divided by $x-1$

use remainder theorem plug $x=1$

$p(1)=1$ so $1$ will be remainder

(b) put $n=2$ you'll get polynomial of degree $(2\times 2018)+(5\times11)=4091$

(c) sum of all coefficients will be also $p(1)$ which is $= 1$