In the world of mathematics, there are two main types of methods of dividing the polynomials the first one is the long division and the second one is the synthetic division. The synthetic division among both of these two methods is considered to be the shortcut method of dividing the polynomials and it is also known as the division of polynomials under a specific case whenever it will be undertaken with the help of linear factors.
This is considered to be the best possible replacement of the long division method and to further perform this particular method we will need to be clear about several kinds of steps associated with the whole process. The synthetic division is the shortcut way of dividing the polynomials very easily and whenever people will be indulging in dividing it will be undertaken with the help of linear factors in the whole process. Generally, this particular method can be used to find out the zeros or roots of the polynomials and note for the division of the factors and the formal definition of this particular method has been explained as:
Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree one and is generally used to find out the zeros of the polynomials.
This particular division method will be perfectly performed manually without any kind of issue in terms of calculation in comparison to the long division method and the binomial term which can be used as the divisor in this method will be known as X – B.
Following are the basic steps which the people need to undertake at the time of performing it:
Whenever the individuals are interested to divide the polynomials with the help of synthetic division they will be going with the option of dividing it with the help of linear expression in the first number of the leading coefficient in this particular area will be one. This particular division will be undertaken with the help of a linear denominator and will also be known as the division through Ruffini’s rule.
The basic requirement to be undertaken at the time of undertaking this particular system has been explained as:
The divisor of the given polynomial should be of degree one and it will mean that exponent of the given variable should be one because such divisor will be known as a linear factor
The commission of the divisor variable for example X will also be equal to 1.
The entire process of synthetic division will be messed up if the divisor of the leading sufficient is other than the one and in case if the leading sufficient of the divisor is other than one while performing the synthetic division method people always need to solve down the problem very carefully and for this purpose people also need to follow a specific mantra which has been explained as:
Bring down, multiply and add, multiply and add, multiply and add and so on
The steps are explained as:
- People need to set up the problem in the form of a denominator is equal to 0 and the numerator will be written into the descending order in the whole process.
- Now the problem will be set up perfectly and people need to bring the first number or the leading coefficient straight down
- After this people need to put the result into the next column by multiplication of the number into the division box with the number which the people have brought down
- Now one will need to write the result into the bottom of the road by adding two numbers together
- This particular state has to be repeated until people reach the end of the problem
- After this one will need to write down the final answer in the whole process
Hence, be clear about the entire procedure of the synthetic division on polynomials is very much important for the people and for further help people can depend on platforms like Cuemath to ensure success.