1. PC – Functions Name ___________________________
Synthetic Division
Although long division is one of our objectives to learn in Precalc and it works when dividing any polynomials,
synthetic division is a very EASY way to factor when we are just dividing by a linear expression. Again, this only
works when dividing by a linear expression when using this method.
In words from Dr. Math:
1. Write “r” down (“r” is the root or x-intercept), and put a line to the right and below it. This represents
the divisor.
2. Further to the right, list the coefficients of the dividend polynomial. Don't forget to put in zeros if
powers of the variable “x” are skipped.
3. Leave a blank line and then draw a horizontal line for the additions to follow.
4. Bring down the first coefficient below the line.
5. Multiply that last number by the number “r” and put it above the line and in the next column to the
right.
6. Add the two numbers in this column, and put the sum in the same column below the line.
7. If we are not out of columns, go back to step 5.
8. Draw a line to the left and below the last number in the last line (boxing in this last number).
9. The quotient is read off from the last line, coefficient by coefficient, left to right, ending at the vertical
line. The power of the quotient decreases by one. The remainder is the last number in the last line
(the boxed number from step 8).
Let’s see an example below before we try on our own!
Taking the bottom line as coefficients we find that the quotient is: 2 − 1 − 3. We will need to
factor this quadratic completely in order to find our other solutions.
+1 2 -3 -2 3
2 -1 -3 0 = R
+
2 -1 -3

2. Now you try! Use this system to accurately factor the polynomials below.