# Polynomial

A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable raised to a certain power and multiplied by a coefficient. For example, the expression x2 + 3x – 5 is a polynomial in the variable x. The term "polynomial" comes from the Greek word for "many parts." What is a polynomial simple definition? A polynomial is an algebraic expression consisting of variables and coefficients, that is, constant numbers. The variables are usually represented by letters x, y, or z. The coefficients are the real numbers that multiply the variables. For example, the expression 3x^2+5x+7 is a polynomial. The degree of a polynomial is the highest power of the variable that appears in the expression. In the example above, the degree of the polynomial is 2.

### What are the 4 types of polynomials?

There are four types of polynomials: linear, quadratic, cubic, and quartic.

A linear polynomial is a polynomial of degree one, meaning that it is a constant plus a multiple of x. For example, 3x + 5 is a linear polynomial.

A quadratic polynomial is a polynomial of degree two, meaning that it is a constant plus a multiple of x squared. For example, x^2 + 3x + 5 is a quadratic polynomial.

A cubic polynomial is a polynomial of degree three, meaning that it is a constant plus a multiple of x cubed. For example, x^3 + 2x^2 + 5 is a cubic polynomial.

A quartic polynomial is a polynomial of degree four, meaning that it is a constant plus a multiple of x to the fourth power. For example, x^4 + 3x^3 + 5 is a quartic polynomial.

### Why it is called polynomial?

A polynomial is a mathematical expression that can be written as a sum of terms, each of which is the product of a constant and a power of a variable. The terms of a polynomial are often referred to as its "coefficients." The degree of a polynomial is the highest power of the variable that appears in the expression. For example, the polynomial x^2 + 3x + 5 has degree 2, since the highest power of the variable x that appears in the expression is 2. The degree of a constant polynomial (one that does not contain any variables) is 0. How can we identify a polynomial? A polynomial is a mathematical expression that is a sum of terms, each of which is a product of a constant and one or more variables raised to a non-negative integer power.

### What is not polynomial?

There are a few different things that could be meant by the question, "What is not polynomial?" For example, it could be asking for a definition of "non-polynomial," or it could be asking for an example of something that is not a polynomial.

Assuming the latter interpretation, an example of something that is not a polynomial is the function

f(x) = begin{cases} x^2 & text{if } x text{ is rational} \ -x^2 & text{if } x text{ is irrational} end{cases}

This function is not a polynomial because it is not continuous at x = 0 (where the two branches of the function meet).