Question

find out the reminder when p(x)=x^4-x^3-2x^3-x+3 is divided by x-3?

Answer 1

Here is the answer=

$p(x)=x^4-x^3-2x^3-x+3\\g(x)=x-3\\x-3=0\\x=3\\p(3)=(3)^4-(3)^3-2(3)^3\\ =81-27-2*27\\ =54-54\\=0$

The remainder is 0 i.e g(x) is a factor of p(x).