Long division 3x+1/6x^6+5x^5+2x^4-9x^3+7x^2-10x+2

We divide first number from first parenthesis with first number from second parenthesis. Then the resulting number we multiply by all numbers in second parenthesis and substract from first parenthesis.



We repeat previous steps until we run out of numbers:



We are left with a number that has no x inside. This is remainder.
The final solution is sum of all these solutions and remainder:

2. root 6 is the right answer