Introduction to Exercise 2.1: Polynomials (Class 9)

In Exercise 2.1, students learn about polynomials and their properties. A polynomial is an algebraic expression made up of terms that involve variables raised to non-negative integer powers, combined with constants or coefficients.

Key Concepts:

1. Definition of Polynomials: A polynomial is of the form P(x) = a_nxⁿ a_n-1x^n-1 + ... + a⁰, where each term consists of a variable raised to a power and multiplied by a constant (coefficient).

2. Types of Polynomials:
- Monomial: A single term ( e.g. 2x³ ).
- Binomial: Two terms ( e.g., x² + 4x).
- Trinomial: Three terms ( e.g., x² + 5x + 6 )

3. Degree of a Polynomial: The degree is the highest power of the variable in the polynomial.

4. Zero Polynomial: A polynomial that has all its coefficients equal to zero.

Class 9 math NCERT Exercise 2.1 involves identifying and working with different polynomials, understanding their degree, and exploring their types and coefficients. It provides a foundational understanding of polynomials for solving algebraic problems.

Exercise 2.1 ( NCERT Math Solution)

1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

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2. Write the coefficients of x² in each of the following:

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3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.

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4. Write the degree of each of the following polynomials:

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5. Classify the following as linear, quadratic and cubic polynomials:

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