Polynomials Class 10

 Polynomials Class 10 

Introduction to Polynomials 

• A polynomial is an algebraic expression made up of variables (like x) and constants, combined using addition, subtraction, multiplication, and non-negative integer powers of variables.

Examples of Polynomialsx

• $x^2 + 3x + 2$
  

• $2x^3 - 5x + 7$
  

• $4$ (a constant polynomial)

Important Terms

1. Degree of a Polynomial

• The highest power of the variable in a polynomial is called its degree.

Examples:

• $x^2 + 3x + 1$ → Degree = 2

• $5x^3 - 2x$ → Degree = 3

2. Types of Polynomials (Based on Degree)

• Linear Polynomial →                                            - Degree 1 (e.g., $2x + 3$)

• Quadratic Polynomial →                                      - Degree 2 (e.g., $x^2 + 5x + 6$)

• Cubic Polynomial →                                             - Degree 3 (e.g., $x^3 - x + 1$)

3. Zeroes of a Polynomial

• A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.

Example:
For $x^2 - 4$

$$x^2 - 4 = 0 \Rightarrow x = \pm 2$$

So, 2 and -2 are zeroes.

Key Idea

- Polynomials are very important in mathematics because they help in:

• Solving equations

• Graphing curves

• Understanding real-life problems in science and engineering

Also read: Polynomials Exercise 2.1 Class 10

Also read: Polynomials Exercise 2.2 Class 10

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