1 | 1 2 -5..3..-1
.....1 1..3 -2...1
.....1 3 -2..1 | 0
Solution is x^3+3x^2-2x+1 and no remainder.
The first figure in the quotient on the bottom line is the same as the first figure in the top line. Multiply this by the divisor, which is 1 because x-1=0 is a potential factor so 1 is the potential root. Write this on the middle line under 2 and add making 3 in the quotient. Multiply 3 by 1 and put the result under the next figure in the dividend, -5, and add to give -2 in the quotient. Multiply -2 by 1 and write the result under the next figure on the top line dividend, 3. Add -2 to 3 to give 1 in the quotient. When we multiply this by 1 and to the last figure -1 we get zero. This is the remainder. It's usual to instead a divider symbol (|) separating the divisor from the dividend and the quotient from the remainder.