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Problem: Synthetic division (3x^3-2x^2+3x-4)/(x-3) [ Calculator, Method and examples ]

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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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