prompter: What is polinom in math?

assistant: If you are referring to a polynomial expression in mathematics, then a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. The word polynomial was derived from the term binomial by replacing the Latin root "bi" with "poly" meaning many in Greek.

Do you have anything else you would like to know regarding polynomials?

prompter: Could you explain with the math formula?

assistant: Sure. Some examples of polynomials may give some clarity
2x^2 + 5x - 7
6x - 1
11x^3 - x
5x^4 + 9x^3 - 2x^2 + 8x + 3

In these examples, x is the variable, the coefficients are the numbers that appear right before x, and the "powers" are the numbers that appear right after ^

Take for example: 2x^2 + 5x - 7
2 is the coefficient of x^2, 5 is the coefficient of x, -7 is called the "constant" term.
We would speak out this polynomial as "two x to the power of two plus five x minus 7"
People will often say "squared" instead of "to the power of two", and "cubed" instead of "to the power of three".

Let's look at one more of the examples: 5x^4 + 9x^3 - 2x^2 + 8x + 3
Spoken aloud this polynomial would be "five x to the power of four plus nine x cubed minus two x squared plus eight x plus 3"
The coefficient of x^4 is 5, the coefficient of x^3 is 9, the coefficient of x^2 is -2, the coefficient of x is 8, and the constant term is 3.

Do you have any further questions regarding polynomials?

prompter: Ok thanks 👍🏼

assistant: Sure, I can provide you with the mathematical formula for a polynomial expression. A general polynomial of degree n can be expressed as:

a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0

Here, x is a variable, a_n to a_0 are constants known as coefficients, and n is a non-negative integer representing the degree of the polynomial. The degree of a polynomial is determined by the highest power of x that appears in the expression.

For example, the polynomial 2x^3 + 3x^2 - 5x + 7 is a third-degree polynomial since the highest power of x is 3.

prompter: Please provide a formula to compute:
$2x^3 + 3x^2 - 5x + 7 = 0$
Is there an easy algorithm to compute the solution, for any third-degree polynomial?

assistant: it is not polinom, it is a polynomial..In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1. this text from wiki
https://en.wikipedia.org/wiki/Polynomial

prompter: Can you give me a response based on another source?

assistant: A polynomial is a mathematical term that consists of a sum of products of coefficients and variables. Some examples are:

* 2x + 3
* 4x² + 3x - 1
* 5xy - 2y^4 + 3x, which is a polynomial with 2 variables.

Polynomials are widely used in many fields of Mathematics such as linear algebra and analysis. They are also used in computer graphics for drawing smooth curves called splines.

assistant: Write Fictional Planet Data in JSON format including name , size , type , atmosphere and description.

prompter: Thanks, that was exactly what I was asking about.
Tell me more.