**CBSE Class 10 Maths Notes Polynomial:-**Download PDF Here

## Class 10 Maths Chapter 2 Polynomial Notes

CBSE Class 10 Maths Chapter 2 Polynomial Notes are provided here in detail. Here, we are going to discuss the complete explanation of what is polynomial and its types, algebraic expressions, degree of a polynomial expression, graphical representation of the polynomial equations, factorization, relationship between zeroes and coefficient of a polynomial, and so on with many examples.

## Algebraic Expressions

An algebraic expression is an expression made up of variables and constants along with mathematical operators.

An algebraic expression is a sum of terms, which are considered to be building blocks for expressions.

A term is a product of variables and constants. A term can be an algebraic expression in itself.

Examples of a term – 3 which is just a constant.

– 2x, which is the product of constant ‘2’ and the variable ‘x’

– 4xy, which is the product of the constant ‘4’ and the variables ‘x’ and ‘y’.

– 5x^{2}y, which is the product of 5, x, x and y.

The constant in each term is referred to as the coefficient.

Example of an algebraic expression: 3x^{2}y+4xy+5x+6 which is the sum of four terms: 3x2y, 4xy, 5x and 6.

An algebraic expression can have **any number of terms**. The **coefficient** in each term can be **any real number**. There can be **any number of variables** in an algebraic expression. The **exponent** on the variables, however, must be **rational numbers.**

To know more about Algebraic Expressions, visit here.

### Polynomial

An algebraic expression can have exponents that are rational numbers. However, a polynomial is an algebraic expression in which the exponent on any variable is a whole number.

5x^{3}+3x+1 is an example of a polynomial. It is an algebraic expression as well.

2x+3√x is an algebraic expression, but not a polynomial. – since the exponent on x is 1/2 which is not a whole number.

To know more about Polynomial, visit here.

### Degree of a Polynomial

For a polynomial in one variable – the highest exponent on the variable in a polynomial is the degree of the polynomial.

Example: The degree of the polynomial x^{2}+2x+3 is 2, as the highest power of x in the given expression is x2.

## Types Of Polynomials

Polynomials can be classified based on:

a) Number of terms

b) Degree of the polynomial.

### Types of polynomials based on the number of terms

a) Monomial – A polynomial with just one term. Example: 2x, 6x^{2}, 9xy

b) Binomial – A polynomial with two terms. Example: 4x^{2}+x, 5x+4

a) Trinomial – A polynomial with three terms. Example: x^{2}+3x+4

### Types of Polynomials based on Degree

**Linear Polynomial**

A polynomial whose degree is one is called a linear polynomial.

For example, 2x+1 is a linear polynomial.

**Quadratic Polynomial**

A polynomial of degree two is called a quadratic polynomial.

For example, 3x^{2}+8x+5 is a quadratic polynomial.

#### For More Information On Quadratic Polynomials, Watch The Below Video.

**Cubic Polynomial**

A polynomial of degree three is called a * cubic polynomial*.

For example, 2x

^{3}+5x

^{2}+9x+15 is a cubic polynomial.

## Graphical Representations

Let us learn here how to represent polynomial equation on the graph.

### Representing Equations on a Graph

Any equation can be represented as a graph on the Cartesian plane, where each point on the graph represents the x and y coordinates of the point that satisfies the equation. An equation can be seen as a constraint placed on the x and y coordinates of a point, and any point that satisfies that constraint will lie on the curve

For example, the equation y = x, on a graph, will be a straight line that joins all the points which have their x coordinate equal to their y coordinate. Example – (1,1), (2,2) and so on.

### Geometrical Representation of a Linear Polynomial

The graph of a linear polynomial is a straight line. It cuts the X-axis at exactly one point.

### Geometrical Representation of a Quadratic Polynomial

^{2}+bx+c

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