Question

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

Answer 1

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