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

Question 820943: Using synthetic division, what is the quotient of f(x)=x^4-x^2+3x; g(x)=x+1
Answer by josgarithmetic(39617) (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.

;
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

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