\(\left(2x^3-9x^2+10x-3\right):\left(x-3\right)\)
\(\dfrac{2x^3-9x^2+10x-3}{x-3}\)
\(=\dfrac{2x^3-6x^2-3x^2+9x+x-3}{x-3}\)
\(=\dfrac{2x^2\left(x-3\right)-3x\left(x-3\right)+\left(x-3\right)}{x-3}\)
\(=\dfrac{\left(2x^2-3x+1\right)\left(x-3\right)}{x-3}\)
\(=2x^2-3x+1\)