<PRE><B>Question 820943</B>
You need to practice in comparison to thoroughly worked examples.


The root which is for g(x) is x=-1.  You indicate this in the divisor location for the synthetic division form.


{{{x^4+0*x^3-1x^2+3x+0}}};
The coefficients are shown on the right side of the division form.

___________|
_______-1__|_____1_____0_____-1_______3________0
___________|
___________|______________________________________





___________|
_______-1__|_____1_____0_____-1_______3________0
___________|
___________|______________________________________
________________1


Bring down the 1 from the dividend; (-1)*1=-1; put this under the next term for the dividend and ADD;


___________|
_______-1__|_____1_____0_____-1_______3________0
___________|
___________|___________-1__________________________
________________1______-1



Do (-1)(-1)=1, put this under the next term of the dividend and ADD:



___________|
_______-1__|_____1_____0_____-1_______3________0
___________|
___________|___________-1____1______________________
________________1______-1_____0



and continuing,
___________|
_______-1__|_____1_____0_____-1_______3________0
___________|
___________|___________-1____1_______0________-3_____
________________1______-1_____0______3________-3



The bottom row of the form is the result of synthetic division, which is interpreted as {{{x^3-x^2+3 + (-3)/(x+1)}}}
</PRE>