What is the difference between polynomial and function

For example sin x, cos x, e x can be approximated using polynomial functions. In the field of statistics, the relationships between variable are approximated using polynomials by finding the best fitting polynomial and determining appropriate coefficients. The exponents are non-negative, and the variables and the coefficients are real.

Therefore, we can say that monomials are summands of polynomials or a single term of the polynomial is a monomial. Coming from Engineering cum Human Resource Development background, has over 10 years experience in content developmet and management. Registration done! Sit and relax as our customer representative will contact you within 1 business day Continue. Forum Algebra what is the difference between polynomial Pushkala Krishnan, 7 years ago.

Enter email id Enter mobile number. Cancel Notify me. A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. An algebraic expression is an expression with a variable in it, and a polynomial is an expression with multiple terms with variables in it.

For practical reasons, we distinguish polynomial equations into four types. A polynomial equation with only one variable term is called a monomial equation. It is also called a linear equation. The algebraic form of a linear equation is of the form:.

A polynomial with two variable terms is called a binomial equation. It can also be called a quadratic equation. The algebraic form of a quadratic equation is of the form:. A polynomial with three variable terms is called a trinomial equation. It is also called a cubic equation. First, since we want to add, subtract and multiply polynomials otherwise, what good are they? Such a set of objects is called a ring Wikipedia link.

So, suppose we have such a set of objects. With this definition, a polynomial is a bit like a matrix. It doesn't 'take input' by itself - that is, to highly pedantic people a polynomial is not a function, but it can represent a function.

If you know some linear algebra, this is a bit like how a matrix is not itself a function, but instead represents a function in particular, a linear transformation with certain choices of bases. The point is that polynomials themselves are 'just' formal expressions which we can manipulate freely; we don't need to be tied down to the somewhat vague notion of 'a variable'.

So how does this relate to the usual definition? In addition to the other excellent answers, I would add that in some contexts especially the contexts that high school students find themselves in , the difference between polynomials and functions can be as simple as the difference between expressions and equations.

It can only be solved when it is an equation, i. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. What is the difference between a polynomial and a function or can they be used interchangebly?