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Find Synthetic division (3x^3-2x^2+3x-4)/(x-3)

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Your problem `->` Synthetic division (3x^3-2x^2+3x-4)/(x-3)


`((3x^3-2x^2+3x-4))/((x-3))` using synthetic division

To determine root divisor, we have to solve divisor equation `x-3=0`

`:.` our root becomes `x=3`

Write coefficients of the dividend `3x^3-2x^2+3x-4` to the right and our root `3` to the left

`3``3``-2``3``-4`
````````


Step-1 : Write down the first coefficient `3`

`3``3``-2``3``-4`
````````
`3`


Step-2 : Multiply our root `3` by our last result `3` to get `9` [ `3` × `3` = `9` ]

`3``3``-2``3``-4`
```9`````
`3`


Step-3 : Add new result `9` to the next coefficient of the dividend `-2`, and write down the sum `7`, [ `(-2)` + `9` = `7` ]

`3``3``-2``3``-4`
```9`````
`3``7`


Step-4 : Multiply our root `3` by our last result `7` to get `21` [ `3` × `7` = `21` ]

`3``3``-2``3``-4`
```9``21```
`3``7`


Step-5 : Add new result `21` to the next coefficient of the dividend `3`, and write down the sum `24`, [ `3` + `21` = `24` ]

`3``3``-2``3``-4`
```9``21```
`3``7``24`


Step-6 : Multiply our root `3` by our last result `24` to get `72` [ `3` × `24` = `72` ]

`3``3``-2``3``-4`
```9``21``72`
`3``7``24`


Step-7 : Add new result `72` to the next coefficient of the dividend `-4`, and write down the sum `68`, [ `(-4)` + `72` = `68` ]

`3``3``-2``3``-4`
```9``21``72`
`3``7``24``68`


We have completed the table and have obtained the following coefficients
`3,7,24,68`

All coefficients, except last one, are coefficients of quotient, last coefficient is remainder.
Thus quotient is `3x^2+7x+24` and remainder is `68`






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