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

Topic

Polynomials

Description

This tutorial introduces complex solutions to polynomial equations, explaining imaginary numbers and the complex number system. It shows how to solve quadratics with no real solutions. Applications include modeling scenarios requiring complex coordinates. Key vocabulary includes complex numbers, imaginary unit, discriminant, and conjugates.

This video is essential to understand the topic of Polynomials. It provides insights into mathematical concepts and their applications, with a focus on building foundational understanding.

Teacher’s Script: Students, as we dive into today’s topic, this video will offer a visual exploration of complex solutions to polynomial equations, explaining imaginary numbers and the complex number system. It shows how to solve quadratics with no real solutions. Applications include modeling scenarios requiring complex coordinates. Key vocabulary includes complex numbers, imaginary unit, discriminant, and conjugates. It’s designed to clarify key points and provide practical examples. Pay close attention to how the concepts are illustrated, as they will be crucial for our upcoming activities.

For a complete collection of videos related to Polynomials click on this link: Polynomials Collection.

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.

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.

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.

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.

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:

This is a polynomial of degree 2:

This is a polynomial of degree 3: