1. Synthetic Division
The shortcut

2. Synthetic Division Process
Only use when dividing by a binomial
Ex: (6x3 – 19x2 + x + 6) / (x – 3)
Make sure all polynomials are in order of descending degree (and include all degrees), then write the coefficients of the dividend horizontally.
Where the binomial is in the form (ax-r), write r/a to the left of the coefficients.
- This means you have to reverse the sign of the second term, like we did with “a” in absolute value equations.

3. Synthetic Division Process (cont.)
Draw a Line below, with space between. Bring the first coefficient below the line.
Multiply the coefficient under the line by r.
Write this product under the second coefficient.
Add.
Multiply the sum by r.
Repeat 5-7.

4. Remainder
The sum of the last coefficient and the r-product is the remainder, which is still written over the divisor (just like in Long Division)