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Synthetic Division


Synthetic division is the method that is used to manually perform the Euclidean division of a polynomial. Division of polygons can be done by using a long division method. But the synthetic method is easier as compared to the long division method as it involves less calculation which makes calculation much easier than before. Here we will learn about the equation that represents the division of two polynomial; p(x) /q(x) = Q + R / (q (x))
p(x) stands for dividend,
q (x) stands for linear divisor,
Q stands for quotient
R stands for the remainder.

Synthetic Division Method

As above we learned about what synthetic division is, now let’s learn about its method. To make this easy and more understanding you can go through the following steps :

  • First, you have to check if the polynomial is in a standard form or not.
  • Then write the coefficient in the dividend’s place and zero of the linear factor in the divisor’s place.
  • Once you are done, then bring the coefficient down and multiply it with the divisor and write the next coefficient below.
  • Now add them and write them below, now repeat the previous two steps until you reach the last term.
  • Now separate the last term, the number which you obtained is the remainder.
  • Now you can group the coefficient with the variable to get the quotient.

How to Solve Synthetic Division

You may find solving synthetic division different as it has different concepts. It uses numbers for calculation while avoiding the use of variables. In this case, despite division, we have to multiply and in place of subtraction, we have to do addition.

Example: The distance covered by Shampy in her scooter is represented by an expression ( x * x) – 2. Time taken by her to cover this distance is also represented by an equation (x + 2) to find the speed of the scooter.

To solve this, we will simply use the formula and put the equations in it, and use the above steps
(x² + x -2) / (x + 2)
Now we will be focusing on numerical calculation ignoring variable
1   +  1  – 2 /
-2       2  = -1
Following the above steps we can find q = ( x-1); r = 0
So the speed is X – 1

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