nothing to "bring down". The polynomial above the bar is the quotient q(x), and the number left over (5) is the remainder r(x). The long division algorithm for arithmetic is very similar to the above algorithm, in which the variable x is replaced (in base 10) by the specific number 10. Polynomial short division Blomqvist's method is an abbreviated version of the long division above. This pen-and-paper method uses the same algorithm as polynomial long division, but mental calculation is used to determine remainders. This requires less writing, and can therefore be a faster method once mastered. The division is at first written in a similar way as long multiplication with the dividend at the top, and the divisor below it. The quotient is to be written below the bar from left to right. Divide the first term of the dividend by the highest term of the divisor (x3 ÷ x = x2). Place the result below the bar. x3 has been divided leaving no remainder, and can therefore be marked as used with a backslash. The result x2 is then multiplied by the second term in the divisor −3 = −3x2. Determine the partial remainder by subtracting −2x2 − (−3x2) = x2. Mark −2x2 as used and place the new remainder x2 above it. Divide the highest term of the remainder by the highest term of the divisor (x2 ÷ x = x). Place the result (+x) below the bar. x2 has been divided leaving no remainder, and can therefore be marked as used. The result x is then multiplied by the second term in the divisor −3 = −3x. Determine the partial remainder by subtracting 0x − (−3x) = 3x. Mark 0x as used and place the new remainder 3x above it. Divide the highest term of the remainder by the highest term of the divisor (3x ÷ x = 3). Place the result (+3) below the bar. 3x has been divided leaving no remainder, and can therefore be marked as used. The result 3 is then multiplied by the second term in the divisor −3 = −9. Determine the partial remainder by subtracting −4 − (−9) = 5. Mark −4 as used and place the new remainder 5 above it. The polynomial below the bar is the quotient q(x), and the number left over (5) is the remainder r(x). Pseudocode The algorithm can be represented in pseudocode