What are polynomials?

Polynomials are mathematical expressions that consist of variables, coefficients, and exponents. They are typically written in the form of a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power. For example, the polynomial 3x^2 + 2x - 5 consists of three terms: 3x^2, 2x, and -5. Polynomials are used in various mathematical operations, such as addition, subtraction, multiplication, and division, and are fundamental in algebra and calculus.

A polynomial is a mathematical expression consisting of the sum of one or more terms, where each term is a constant multiplied by a variable raised to a non-negative integer power.

General Form:

```
P(x) = a_n-x^n + a_{n-1}-x^{n-1} + ... + a_2-x^2 + a_1-x + a_0
```

where:

- P(x) is the polynomial
- x is the variable
- a_n, a_{n-1}, ..., a_0 are constants called coefficients
- n is the degree of the polynomial

Key Properties:

- The degree of a polynomial is the highest exponent of the variable in any term.
- Polynomials can be added, subtracted, multiplied, and divided by other polynomials.
- The roots of a polynomial are the values of x that make the polynomial equal to zero.
- Polynomials have a variety of applications, such as:
- Modeling relationships between variables
- Solving equations
- Approximating functions

Example:

```
P(x) = 2x^3 - 5x^2 + 7x - 4
```

- Degree: 3
- Coefficients: a_3 = 2, a_2 = -5, a_1 = 7, a_0 = -4