# How do you use synthetic division to find f(sqrt{3}) if f(x)=2x^3-6x+5?

In this case we would just do synthetic division using the value $\sqrt{3}$ and the value of $f \left(x\right)$ at that x value will be the remainder, $r \left(x\right)$.
In this case if you did everything right, $q \left(x\right)$ should equal $2 {x}^{3} + 2 \sqrt{3} {x}^{2}$ and the most important part, $r \left(x\right)$, should equal $5$.