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

It is enough to evaluate the dividend polynomial at $x = a$ where $a$ is a root of the divisor polynomial . In this case $R \left(x\right) = 0$
So in this case $D \left(x\right) = {x}^{3} - x + 6$ and 2 is the root of the divisor $d \left(x\right) = x - 2$
The remainder is just $D \left(2\right) = {2}^{3} - 2 + 6 = 0$.