Introduction to Polynomials

A series of free, online Intermediate Algebra Lessons or Algebra II lessons, with videos, examples, and solutions.
In these lessons, we will learn

  • what are polynomials
  • about polynomial functions

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The following diagrams show the types of polynomial according to the number of terms: monomials, binomials, trinomials, polynomials and the degree of a polynomial. Scroll down the page for more examples and solutions on how to define polynomial functions.


Introduction to Polynomials

Before adding and subtracting polynomials or multiplying polynomials, it is important to have an introduction to polynomials with a definition of a polynomial and polynomial vocabulary. Important polynomial definitions include terms, monomial, the degree of a monomial, polynomial degree and standard form.

What is a term?
A term can be a number, a variable, a product of numbers and/or variables, or a quotient of numbers and/or variables.

What is a monomial?
A monomial is a real number and/or the product of variables with non-negative exponents.

What is a polynomial?
A polynomial is a monomial or a sum of monomials. Remember that subtraction can be rewritten as addition.

What is the degree of a term?
The degree of a term is the number of variable factors in the term. You can also say the degree of a term is the sum of the exponents on the variables.

What is the degree of a polynomial?
The leading term of a polynomial is the term of highest degree.
The degree of a polynomial is the same as the degree of the leading term.

How to talk about polynomials?

Polynomial Functions

A polynomial function is a function comprised of more than one power function where the coefficients are assumed to not equal zero. The term with the highest degree of the variable in polynomial functions is called the leading term. All subsequent terms in a polynomial function have exponents that decrease in value by one.

How to evaluate a polynomial in function notation.

How we define polynomial functions, and identify their leading coefficient and degree?
Polynomial Fundamentals (Identifying Polynomials and the Degree)
We look at the definition of a polynomial. We the practice identifying whether a function is a polynomial and if so what its degree is using 8 different examples.

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