# What defines a polynomial function?

Table of Contents

## What defines a polynomial function?

A polynomial is a function of the form f(x) = anxn + an−1xn−1 + + a2x2 + a1x + a0 . The degree of a polynomial is the highest power of x in its expression. Constant (non-zero) polynomials, linear polynomials, quadratics, cubics and quartics are polynomials of degree 0, 1, 2 , 3 and 4 respectively.

**What kind of polynomial is P?**

1 Answer. p(x) is a polynomial of degree 1.

### Which one is not polynomial?

(d) 2x−5x is also not a polynomial, since the exponents of variable in 1st term is a rational number.

**How do you classify polynomials?**

Polynomials can be classified by the degree of the polynomial. The degree of a polynomial is the degree of its highest degree term. So the degree of 2×3+3×2+8x+5 2 x 3 + 3 x 2 + 8 x + 5 is 3. A polynomial is said to be written in standard form when the terms are arranged from the highest degree to the lowest degree.

## Which of following is a polynomial?

Every monomial, binomial, trinomial is a polynomial. Was this answer helpful?

**What are the characteristics of polynomial functions?**

Recognizing Characteristics of Graphs of Polynomial Functions. Polynomial functions of degree 2 or more have graphs that do not have sharp corners; recall that these types of graphs are called smooth curves. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous.

### How do you know if it’s not a polynomial?

Polynomials cannot contain fractional exponents. Terms containing fractional exponents (such as 3x+2y1/2-1) are not considered polynomials. Polynomials cannot contain radicals. For example, 2y2 +√3x + 4 is not a polynomial.

**How do you describe polynomial equation?**

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.

## Which of the is not a polynomial function?

**What are the parts in polynomial function?**

Important parts of a polynomial function include the degree, the leading term, the leading coefficient, and the constant term.

### What makes a function not a polynomial?

All the exponents in the algebraic expression must be non-negative integers in order for the algebraic expression to be a polynomial. As a general rule of thumb if an algebraic expression has a radical in it then it isn’t a polynomial.

**Which is not a polynomial function?**

Rules: What ISN’T a Polynomial Polynomials cannot contain division by a variable. For example, 2y2+7x/4 is a polynomial because 4 is not a variable. However, 2y2+7x/(1+x) is not a polynomial as it contains division by a variable. Polynomials cannot contain negative exponents.

## How did you classify a polynomial?

A polynomial featuring only one term can be classfied as a monomial. If the polynomial contains 2 terms, it can be classified as a binomial. If the polynomial contains 3 terms, it can be classified as a trinomial.

**Which of the following does not define a polynomial?**

The short answer is that polynomials cannot contain the following: division by a variable, negative exponents, fractional exponents, or radicals.

### What are the key features of a polynomial function?

A polynomial function consists of either zero or the sum of a finite number of non-zero terms, each of which is a product of a number, called the coefficient of the term, and a variable raised to a non-negative integer power.

**What makes an equation a polynomial equation?**