What are Polynomials

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Polynomials are the expressions which contain single term, two terms or more than two terms of numbers and variables combined together by any of the basic operations such as addition, subtraction, multiplication or division. However for a given expression to be a polynomial, it should follow one rule. There should not be any variable placed in the denominator, and if it is placed then it is no longer called a polynomial. Therefore the variables are placed in the numerator and even if the expression contains many terms, it is still called a polynomial.

Example 1: Is the given expression, 7x + 4 – 3x + 10 a polynomial? Simplify the given expression.

Given expression: 7x + 4 – 3x + 10

Since the variable ‘x’ is not placed in the denominator hence yes, the given expression is a polynomial.

In order to simplify the above expression, we have to combine the like terms.

Like terms are the terms which are either plain numbers or are the terms which contain the same variable.

This implies 7x+ 4- 3x+ 10 = 7x- 3x+ 4+ 10==>4x + 14 is the simplified form!

Example 2: Is the given expression, 2x+ 3y+ 5x- 9y- 5a polynomial? Simplify the given expression.

Given expression: 2x+ 3y+ 5x- 9y- 5

Since the variables ‘x’ or ‘y’ is not placed in the denominator hence yes, the given expression is a polynomial.

In order to simplify the above expression, we have to combine the like terms.

This implies 2x + 3y + 5x- 9y- 5= 2x + 5x + 3y- 9y- 5->7x- 6y - 5 is the simplified form!


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