Substitute the value of x = -1 into the polynomial.
The value of the polynomial then will give you the remainder
3*(-1)^100 + 5*(-1)^95 - 4*(-1)^38 + 2*(-1)^17 = 3*1 + 5*(-1) - 4*1 + 2*(-1) = 3 - 5 - 4 - 2 = -8. ANSWER
It is based on the Remainder Theorem.
Theorem (the remainder theorem)
1. The remainder of division the polynomial by the binomial is equal to the value of the polynomial.
2. The binomial divides the polynomial if and only if the value of is the root of the polynomial , i.e. .
3. The binomial factors the polynomial if and only if the value of is the root of the polynomial , i.e. .
