Use synthetic division to determine if the given value for kk is a zero of this polynomial. if not, determine p( k )p( k ).
p(x) = 3x3 − 6x2 − 8x − 19; k = 3

3 | 3 ... -6 ... -8 ... -19
.. | .. ...  9  ..  9 ....    3
- - - - - - - - - - - - - - - -
.. | 3 ...  3 ...  1 ....  -16

which means



which is to say that is not divisible by , and so is not a root. This in turn means .

Indeed, you have



If you were familiar with the polynomial remainder theorem, you would have known this immediately from determining the remainder alone.