The division here can be done by synthetic division or by long division. Either way you get the same result. The attachment shows synthetic division.
The zero of the binomial divisor is placed on the middle row at the left. this is used to multiply the numbers in the bottom row to form the product on the middle row in the next column over. 10 = 2×5, for example. Then the numbers on the bottom row are the sum of the top and middle rows. The top row of numbers is the list of coefficients of the dividend polynomial, highest-to-lowest degree.
The result in the bottom row tells you the quotient from the division is
