How do you use the remainder theorem to find the remainder for each division #(x^3-x+6)div(x-2)#?

1 Answer
Nov 26, 2016

It is enough to evaluate the dividend polynomial at #x=a# where #a# is a root of the divisor polynomial . In this case #R(x)=0#

Explanation:

So in this case #D(x)=x^3-x+6# and 2 is the root of the divisor #d(x)=x-2#
The remainder is just #D(2)=2^3-2+6=0#.
If the remainder in zero it means that the divisor is a factor of the dividend or in other terms that the division is exact