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What Are Polynomials? Video Lecture | Mathematics Olympiad for Class 9

FAQs on What Are Polynomials? Video Lecture - Mathematics Olympiad for Class 9

1. What are polynomials?

Ans. Polynomials are algebraic expressions that consist of variables, coefficients, and exponents. They are made up of one or more terms, which are separated by addition or subtraction operators. Each term can contain a combination of variables raised to non-negative whole number exponents and coefficients, which are usually real numbers.

2. How do you classify polynomials?

Ans. Polynomials can be classified based on the number of terms they contain. If a polynomial has one term, it is called a monomial. If it has two terms, it is called a binomial, and if it has three terms, it is called a trinomial. Polynomials with more than three terms are generally referred to as simply polynomials.

3. What is the degree of a polynomial?

Ans. The degree of a polynomial is determined by the highest exponent present in any of its terms. For example, if a polynomial has terms with exponents 3, 2, and 1, then the degree of the polynomial is 3. The degree helps in understanding the behavior and complexity of the polynomial.

4. How do you add and subtract polynomials?

Ans. To add or subtract polynomials, you need to combine like terms. Like terms are those that have the same variables raised to the same powers. Simply add or subtract the coefficients of the like terms while keeping the variables and exponents unchanged. It is important to ensure that all terms are arranged in descending order of degree before performing the addition or subtraction.

5. Can polynomials have negative exponents?

Ans. No, polynomials cannot have negative exponents. The exponents in polynomials must always be non-negative whole numbers. Negative exponents are allowed in algebraic expressions but not in polynomials. If a polynomial contains a term with a negative exponent, it is not considered a polynomial but rather a rational function.

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Sep 10, 2025 Last updated

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