Question

Using synthetic division how do i find the quotient and remainder

(12x^4+5x^3+3x^2-5)/(x+1)

Answer 1

start by setting up the coefficients for synthetic division process

Answer 2

-1 | 12 5 3 0 -5
|
------------------------------------

Answer 3

seen this before ?

Answer 4

yeah looks familiar now

Answer 5

good :)
step 1 : drop the 12 down to the last row :

-1 | 12 5 3 0 -5
|
------------------------------------
12

Answer 6

then don't you bring 12 up to the next?

Answer 7

step2 : multuply -1*12 and put the result in the next column :

-1 | 12 5 3 0 -5
| -12
------------------------------------
12

Answer 8

step3 : add "5, -12" and put the result down in the last row :


-1 | 12 5 3 0 -5
| -12
------------------------------------
12 -7

Answer 9

just repeat step2 and step3 till the end..

Answer 10

I got -1|
| 12 -7 10 10 -15?

Answer 11

Very good try ! but looks like there is a mistake, let me show u the work

Answer 12

remainder is 5

Answer 13

-1 | 12 5 3 0 -5
| -12 7 -10 10
------------------------------------
12 -7 10 -10 5

Answer 14

oooooh okay

Answer 15

would the remainder be -1 ?

Answer 16

remainder = last number in the last row

Answer 17

oooooh haha yikes thanks

Answer 18

-1 | 12 5 3 0 -5
| -12 7 -10 10
------------------------------------
12 -7 10 -10 | 5

Answer 19

and the quotient ?

Answer 20

remainder = 5

Answer 21

quotient is formed by the coefficients in the last row :

12x^3 - 7x^2 + 10x - 10