1. Pre Calculus – Synthetic Division Unit 3

3. First, you have to write the coefficients of the polynomial to be divided at the top (remember to use 0’s for place holdings) You place the k value (recall x – k ) down to the left of our partial box Drop the coefficient “a” down. Multiply k by the a and add that to b in column 2 Take that answer and multiply it by k and add it to what is in column “c” See the chart below:

4. First, you have to write the numerators coefficients: 5 -17 -12 Second, the divisor is in the form: x – k and you have to find what k = (x – k) = (x – 4) so therefore k = 4 The next slide shows the format

8. The Factor Theorem: A polynomial f(x) has a factor (x - k) if and only if f(k) = 0. In Summary: The remainder "r", obtained in the synthetic division of f (x) by (x - k) provides the following information: 1. the remainder "r" gives the value of "f" at x = k. That is r = f (k) 2. If r = 0, then (x - k) is a factor of f (x) 3. If r = 0, then (k, 0) is an x-intercept of the graph of f (x).

11. Now try a few of your own