In the world of mathematics, there are two types of methods of dividing the polynomials and the first one is the long division method. The second one is the synthetic division method and both of these methods are considered to be the best possible ways of dividing the polynomials. However, the shortcut method is considered to be the Synthetic division method and it is also known as the polynomial division method of a special case when it has to be divided with the help of a linear factor. This particular concept is very much successful in terms of completely replacing the long division method and in some of the situations people will also find this particular method quite easier in comparison to the other one.
The synthetic division is the utilisation of linear factor in terms of dividing the polynomial and is very well utilised in terms of ensuring that people will be able to find out the zeros and roots of the polynomials very easily and not for the division of factors. Hence, the synthetic division is defined as the simplified way of dividing the polynomial with another polynomial equation of degree one that can be used in terms of finding the zeros of the polynomials.
This particular concept is normally performed manually with very less amount of calculation in the whole process and the binomial term is always used as a divisor in this method for example X – B.
What is the process of performing the synthetic division?
If the people are interested to divide the polynomials with the help of this particular method then they need to start it by dividing with a linear expression and the first number of the leading coefficient should be a 1. This particular division method is also known as Ruffini’s rule which is based upon pencil and paper computation systems. People also need to fulfil different kinds of requirements at the time of performing this particular method and those requirements are mentioned as follows:
The divisor of the given polynomial should be of degree one and it means that the exponent of the given variable should be one.
The coefficient of the divisor for example any kind of variable should be equal to one.
The process of synthetic division will always get messed up if the divisor of the leading sufficient is other than the one in the very basic rule which the kids need to follow in the whole process is to bring down, multiply, add, multiply-add, multiply-add and so on this particular process will be continued till the correct answers are achieved.
Following are some of the very basic advantages of depending on this particular method:
- It will always include very few calculation steps.
- The calculation can be very perfectly performed without variables
- Unlike the polynomial long division method, this particular method is very less prone to errors on the behalf of kids.
The steps of calculating the answers with the help of this method are explained as follows:
- People need to set the denominator is equal to 0 and then put the number into the division box and then use the numerator in descending order to check out if any missing terms are there.
- Now one will need to set up the problem perfectly and bring the first number straight down.
- Now one will need to put the result into the next column by multiplying the number into the division box with the number which has been brought down.
- Then people need to write the result at the bottom of the number by adding two numbers together and then until they reach the end of the problem steps have to be repeated.
- Now people can write down the final answer very easily.
Further being clear about the overall process of enrolling the kids on platforms like Cuemath is a good idea so that they become experts of the degree of polynomial and synthetic division systems very easily.