Polynomials Class 10 Basics of Chapter 2

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, combined using the operations of addition, subtraction, and multiplication. The variables in a polynomial are raised to non-negative integer powers. In other words, a polynomial is a sum of terms, where each term consists of a coefficient multiplied by a variable raised to a non-negative integer exponent.

Polynomials can have various degrees. Here are some examples of polynomials of different degrees:

1. Linear Polynomial:  The degree is 1.
2. Quadratic Polynomial:P(x)=ax2+bx+c, where a, b, and c are constants. The degree is 2.
3. Cubic Polynomial: P(x)=ax3+bx2+cx+d, where a, b, c, and d are constants. The degree is 3.
4. Quartic Polynomial: P(x)=ax4+bx3+cx2+dx+e, where a, b, c, d, and e are constants. The degree is 4.

Polynomials are used extensively in mathematics and various scientific and engineering fields for modeling and solving equations, approximating functions, and more.