SOLUTION: P(x) = x3 + 8x2 − 2x + 3, D(x) = x − 4. How do I solve it with the synthetic formula?

Algebra ->  Trigonometry-basics -> SOLUTION: P(x) = x3 + 8x2 − 2x + 3, D(x) = x − 4. How do I solve it with the synthetic formula?      Log On


   

Question 947219: P(x) = x3 + 8x2 − 2x + 3, D(x) = x − 4. How do I solve it with the synthetic formula?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
EDIT: Corrected mistake in the remainder of the final answer.

The root being checked is +4.
The second line or row is for the coefficients, except for here also including the root being checked at the left side.

Format representation:

_______________|_______
_______________|___________________________________________
__________+4___|_______1______8_______-2______3______
_______________|
_______________|___________________________________________


Bring down the first coefficient, multiply by (+4), put this under the second coefficient:
_______________|______________
_______________|___________________________________________
__________+4___|_______1______8_______-2______3______
_______________|______________4
_______________|___________________________________________
_______________________1

ADD the 8 and 4, being 12.

_______________|______________
_______________|___________________________________________
__________+4___|_______1______8_______-2______3______
_______________|______________4
_______________|___________________________________________
_______________________1______12

What is 12%2F4?
3; put this above the 8;


_______________|______________3
_______________|___________________________________________
__________+4___|_______1______8_______-2______3______
_______________|______________4
_______________|___________________________________________
_______________________1______12


Continuing the process until finished:

_______________|______________3_______48_____47.5
_______________|___________________________________________
__________+4___|_______1______8_______-2______3______
_______________|______________4_______192____190
_______________|___________________________________________
_______________________1______12______190____193

The meaning of this is 3x%5E2%2B48x%2B47.5%2B193%2F%28x-4%29.
The very top line shows the quotient coefficients.
Remainder is 193.