SOLUTION: Using synthetic division, what is the quotient of f(x)=x^4-x^2+3x; g(x)=x+1

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Question 820943: Using synthetic division, what is the quotient of f(x)=x^4-x^2+3x; g(x)=x+1
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E4%2B0%2Ax%5E3-1x%5E2%2B3x%2B0;
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%5E3-x%5E2%2B3+%2B+%28-3%29%2F%28x%2B1%29