Скачать или смотреть Chapter -2 Polynomials class 10th maths | 2024-25| All concept & Ex.2.1 Solution

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A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form looks like this:

P(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0

Here’s a quick breakdown:

1. Terms: Each part of the polynomial, like (a_n x^n), is called a term.
2. Coefficients: These are the (a_n, a_{n-1}, \ldots, a_0) values. They are the constants that multiply the variables.
3. Degree: The highest power of the variable (in this case, (n)) determines the polynomial’s degree. For example, in (4x^3 + 3x^2 - 2x + 1), the degree is 3.
4. Variables: The symbols like (x) or (y) that represent numbers in the expression.

Polynomials are foundational in algebra and appear everywhere in math, science, and engineering. They help in solving equations, modeling real-world situations, and even in computer graphics.

Key Properties of Polynomials:

• Addition and Subtraction: You can add or subtract polynomials by combining like terms.
• Multiplication: To multiply polynomials, distribute each term in the first polynomial to every term in the second.
• Factoring: Breaking down a polynomial into simpler “factor” polynomials that, when multiplied, give back the original polynomial.
• Roots/Zeros: Solutions to the polynomial equation (P(x) = 0). These are the values of x where the polynomial equals zero.