*What is a Polynomial?*

Any Algebraic Expression with more than one term is called as the Polynomial, provided it does not have any term with a negative or non-negative exponent for any of the variables. Polynomial is an algebraic Expression the exponents of the variable in which are always non-negative integers.

For Example:

1. X^{2 }+ 3xy + y^{2 }+ 5x^{2}y + 4xy^{2 }

2. 3a^{2}b + 5ab + 4a^{2 }+ 5ab^{2 }

3. X^{4} + 3x^{3} + 4x^{2} + 5ab^{2 }

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*Polynomial in one-variable*

The Algebraic Expression in which we have only one variable.

1. P^{5} + 3p^{4} + 5p^{2} +4p +5

2. 3x^{2} + 5x + 6

*Polynomial with many variables*

These are the polynomial with the different variables.

1. 3x^{2}y + 4x^{2}y + x^{3} +y^{3}

2. X^{4} + y^{4}

*Types of Polynomials are :*

Linear Polynomial : The Polynomial with the degree 1 is called as Linear Polynomial.

Examples:

1. 3x + 7

2. 5x + 4y

3. 7x + y + 3

Quadratic Polynomial : The Polynomial with the degree 2 is called as Quadratic Polynomial.

Example:

1. X^{2} + 5x + 6

2. 3 + xy + y^{2}

Cubic Polynomial : The Polynomial with the degree 3 is called as cubic Polynomial.

Example:

1. 5x^{3} + 3x

2. 4y^{3} – 2

3. 3z^{3 }

^{ }*Like Terms*

Like terms are the ones with the same variable.

7x, 8x, and 9x are the Like terms as they have the same variable.

On the other hand,

7a, 8b and 9c are not the Like terms as they do not have the same variable.

*Adding the Polynomials*

Addition of the Polynomial can be done by combining Like Terms. Example:

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*Subtracting Polynomials*

Consider the Following Examples:

The Subtraction of the polynomials is done after changing the sign with each term, for second equation. Changing the signs of the equation:

Subtracting the equation 1 and 3 now. Equation 3 is new one.

*Are you clear? Yes..? Try some questions then:*

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