Video Tutorial--Polynomial Concepts--Binomial Theorem

Topic

Polynomials

Description

This segment introduces the binomial theorem and its formula for expanding binomials to any power. It connects coefficients with combinations and factorials, showing how exponents and coefficients correlate. Examples use Pascal's triangle and the combination formula to explain the distribution of terms. Key concepts include binomial theorem, factorial, and summation symbol. Applications include deriving coefficients for binomials efficiently and solving polynomial problems in algebra.

The relevance of this video to the topic of Polynomials lies in its ability to contextualize abstract mathematical concepts through visual models and real-world applications. This helps students better understand the foundational principles of polynomials, particularly as they relate to operations and problem-solving.

Teacher's Script: Today, we'll watch a video that explains a key concept in mathematics. This will help you understand how mathematical principles, like those we’re studying now, are applied. Pay close attention to the examples used in the video, especially as they relate to the topic we’ve been exploring.

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: