Polynomials

 

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Video Tutorial--Polynomial Concepts--Video 10--Polynomials with Complex Solutions

Video Tutorial--Polynomial Concepts--Video 10--Polynomials with Complex Solutions

What Are Polynomials?

Polynomials Are Made Up of Monomials

A monomial is a single expression that is usually the product of a number and one or more variables raised to a positive exponent power. Read the following definition.

The definition of a monomial.

A monomial is an example of a polynomial.

Binomials Are Made Up of Two Monomials

If you combine two monomials, you have a binomial, so long as the two monomials cannot be further added or subtracted. Read the following definition.

The definition of a binomial.

Notice how each binomial is made up of two monomials. Here’s an example of two monomials that, when combined, result in a monomial, not a binomial.

The sum of two monomials.

Trinomials Are Made Up of Three Monomials

If you combine three monomials, you have a trinomial, so long as the monomials cannot be further added or subtracted. Read the following definition.

The definition of a trinomial.

Notice how each binomial is made up of three monomials. 

The Degree of a Polynomial

The term with the highest exponent determines the degree of the polynomial.

This is a polynomial of degree 1:

A polynomial of degree 1.

This is a polynomial of degree 2:

A polynomial of degree 2.

This is a polynomial of degree 3: 

A polynomial of degree 3.



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Common Core Standards CCSS.MATH.CONTENT.HSN.CN.C.8
Duration 5.5 minutes
Grade Range 9 - 12
Curriculum Nodes Algebra
    • Polynomials
        • Polynomial Expressions
        • Polynomial Functions and Equations
Copyright Year 2021
Keywords polynomials, polynomial functions, polynomial equations, Complex Number, Complex Conjugate