We want to divide 3x^3 + 2x - 5 by x - 1
THe polynomial can be rewritten as
3x^3 + 0x^2 + 2x - 5
The synthetic division steps are shown below
The first row would contain the coefficients of the polynomial. Thus, we have
3, 0, 2 - 5
We divided by x = 1
The first step was to bring the first coefficient which is 3 downwards. Then we multiplied by 1 to get 3. We added 0 to 3 and got 3 which was brought 3 downwards. The process continued until we got zero. This means that the remainder is zero. The quotient is formed from the numbers at the bottom and they are the coefficients of the quotient. Thus,
Quotient = 3x^2 + 3x + 5
Remainder = 0