In mathematics, there are two methods for dividing polynomials. The first is the long division method. The synthetic division method is another. The synthetic division method is the quickest way to divide polynomials of these two methods. When dividing by the linear factor, it is also known as the polynomial division method of a special case. It takes the place of the long division method. This method may be more convenient in certain circumstances. for more information visit here Online Cricket Betting ID.
Have You Heard of Polynomials?
Polynomials are algebraic expressions with variables and coefficients. Variables are also known as indeterminates. For polynomial expressions, we can perform arithmetic operations such as addition, subtraction, multiplication, and positive integer exponents, but not division by variable. x-12 is an example of a polynomial with one variable. There are three terms in this example: x, and -12.
The term polynomial is derived from the Greek words ‘poly’ meaning “many” and ‘nominal’ which means “terms,” so it means “many terms.” A polynomial can have any number of terms, but it cannot have an infinite number of terms.
What is the Synthetic Division?
The synthetic division is known to be one of the methods used in algebra to perform the Euclidean division of polynomials manually. We can use the long division method to divide polynomials. However, when compared to the long division method of polynomials, the synthetic division method necessitates less writing and fewer calculations. That is, for the special cases where the dividing by a linear factor, the synthetic division is the shorter method of the traditional long-division of a polynomial.
Let us examine the method for performing synthetic division of polynomials in depth using solved examples. for more details about gaming you can visit here Cricket ID.
How Does Synthetic Division Work?
Synthetic division of polynomials is a method of calculating polynomials that do not use variables. Instead of dividing, we multiply, and instead of subtracting, we add. To understand it in a fun way, you may also visit cuemath.com
- Dividend coefficients should be written, and the linear factor’s zero should be used in place of the divisor.
- Now bring down the first coefficient and then multiply it by the divisor.
- Substitute the product for the second coefficient and add the column.
- Repeat until you reach the last coefficient. The final number is used as the remainder.
- Write the quotient using the coefficients.
- It is worth noting that the resultant polynomial is one order lower than the dividend polynomial.
Polynomial Synthetic Division Method Steps
The steps for Synthetic Division of a Polynomial are as follows:
- The first step – To begin, we must set the denominator to zero in order to find the number to enter into the division box. The numerator is then written in descending order, and if any terms are missing, a zero is used to fill in the missing term. Finally, in the division problem, only list the coefficient.
- Step 2 – Once the problem is perfectly set up, bring the first number or leading coefficient straight down.
- Step 3 -Then, in the next column, multiply the number in the division box by the number you brought down.
- Step 4 Add the two numbers together to get the result, which you should write at the bottom of the row.
- Step 5 Repeat steps 3 as well as 4 until you reach the end of the problem.
- Step 6: Compose your final response. The numbers in the bottom row, with the last number being the remainder, yield the final answer, which is written as a fraction. The variables must begin with one power less than the true denominator and decrease by one with each term.
Synthetic Division Method Benefits and Drawbacks
The following are the benefits of using the synthetic division method:
- The method only takes a few steps to calculate.
- The calculation can be carried out without the use of variables.
- This method, as opposed to the polynomial long division method, is less prone to errors.
- One disadvantage of the method – it can only be used if the divisor of the polynomial expression is a linear factor.