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01 - Polynomials for Beginners - Class 10 - Maths Video Lecture

FAQs on 01 - Polynomials for Beginners - Class 10 - Maths Video Lecture

1. What are polynomials?

Ans. Polynomials are algebraic expressions that consist of variables, coefficients, and exponents. They are composed of one or more terms, where each term can be a constant, a variable, or a combination of both. Examples of polynomials include 2x^2 + 3x - 1 and 4y^3 - 2y + 5.

2. How do you classify polynomials based on the number of terms?

Ans. Polynomials can be classified based on the number of terms they have. A polynomial with one term is called a monomial, such as 3x or 7y^2. A polynomial with two terms is called a binomial, for example, 4x^2 + 2y. A polynomial with three terms is called a trinomial, like 2x^3 - 5x^2 + 3.

3. What is the degree of a polynomial?

Ans. The degree of a polynomial is the highest power of the variable present in the polynomial. To find the degree, we look at the exponent of the variable in each term and choose the highest one. For example, in the polynomial 3x^2 + 4x - 1, the highest power of x is 2, so the degree of the polynomial is 2.

4. How do you add or subtract polynomials?

Ans. To add or subtract polynomials, we combine like terms. Like terms have the same variables raised to the same powers. We add or subtract the coefficients of these like terms while keeping the variables and their exponents unchanged. For example, to add the polynomials 2x^2 + 3x - 1 and 4x^2 - 2x + 5, we add the coefficients of the like terms: (2x^2 + 4x^2) + (3x - 2x) + (-1 + 5) = 6x^2 + x + 4.

5. How do you multiply polynomials?

Ans. To multiply polynomials, we use the distributive property and multiply each term of one polynomial by each term of the other polynomial. We then combine like terms to simplify the resulting expression. For example, to multiply the polynomials (2x + 3) and (4x - 1), we multiply each term: (2x * 4x) + (2x * -1) + (3 * 4x) + (3 * -1) = 8x^2 - 2x + 12x - 3 = 8x^2 + 10x - 3.

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