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Method and examples
Method :
Polynomial Synthetic division calculator
Polynomial-1 Polynomial-2
 
SolutionHelp
Polynomial Synthetic division calculator
1. x2-10x+25 and x-5
2. x3+4x2-4x-16 and x-2
3. x3+6x2+12x+10 and x+2


Example
1. Find synthetic division of x2-10x+25 and x-5

Solution:
x2-10x+25x-5 using synthetic division

To determine root divisor, we have to solve divisor equation x-5=0

:. our root becomes x=5

Write coefficients of the dividend x^2-10x+25 to the right and our root 5 to the left

51-1025


Step-1 : Write down the first coefficient 1

51-1025
1


Step-2 : Multiply our root 5 by our last result 1 to get 5 [ 5 × 1=5 ]

51-1025
5
1


Step-3 : Add new result 5 to the next coefficient of the dividend -10, and write down the sum -5, [ (-10) + 5=-5 ]

51-1025
5
1-5


Step-4 : Multiply our root 5 by our last result -5 to get -25 [ 5 × (-5)=-25 ]

51-1025
5-25
1-5


Step-5 : Add new result -25 to the next coefficient of the dividend 25, and write down the sum 0, [ 25 + (-25)=0 ]

51-1025
5-25
1-50


We have completed the table and have obtained the following coefficients
1,-5,0

All coefficients, except last one, are coefficients of quotient, last coefficient is remainder.
Thus quotient is x-5 and remainder is 0




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