Given p(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. use synthetic division to find the quotient and the remainder.

You can find the remainder right away by simply plugging in . The polynomial remainder theorem guarantees that the value of is the remainder upon dividing by , but I digress...

Synthetic division yields

3   |   2   -11   18   -15
.    |           6   -15     9
- - - - - - - - - - - - - - - - -
.    |   2     -5     3     -6

which translates to



(and note that , as expected)

The first option would be correct if it were one half and not one