When the function $f(x)$ is divided by $x-2$, the quotient is $3 x^{2}-x+7$ and the remainder is -10 . Find the function $f(x)$ and write the result in standard form.

Step 1 ：The problem provides that when the function $f(x)$ is divided by $x-2$, the quotient is $3x^2 - x + 7$ and the remainder is -10.

Step 2 ：We know from the polynomial division that if a polynomial $f(x)$ is divided by $x-a$ to give a quotient $q(x)$ and a remainder $r$, then $f(x) = (x-a)q(x) + r$.

Step 3 ：In this case, $a=2$, $q(x) = 3x^2 - x + 7$, and $r=-10$.

Step 4 ：We can substitute these values into the formula to find $f(x)$.

Step 5 ：So, $f(x) = (x-2)(3x^2 - x + 7) - 10$.

Step 6 ：Simplify the expression to get $f(x) = 3x^3 - 7x^2 + 9x - 24$.

Step 7 ：Final Answer: The function $f(x)$ is \(\boxed{3x^3 - 7x^2 + 9x - 24}\).