Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Learn it your way
A short class with Sarah and her students. The other ways are under More.
Sign up free to listen. Transcripts are free to read.
Today we will learn about polynomials in one variable. Can anyone tell me what a polynomial is?
Isn't it just a mathematical expression involving sums and products?
Yes, but specifically, a polynomial is an expression that includes terms like these: ax^n, where a is a coefficient and n is a non-negative integer. Can anyone give an example?
x² + 5x + 6 is a polynomial!
Exactly! And how many terms does this polynomial have?
It has three terms!
Excellent! So we classify polynomials by the number of terms. We've got monomials, binomials, and trinomials. Remember this with the acronym M-B-T!
Got it! M stands for monomials, B for binomials, and T for trinomials!
Great! Let's move on to the degrees of these polynomials.
Let's summarize what we've learned today about polynomials in one variable. What are the types of polynomials?
Monomials, binomials, and trinomials!
And we discussed the degrees and zeroes of polynomials too.
That's right! Remember that the degree tells us about the polynomial's leading behavior and that zeros are vital for factorization. Excellent class today, everyone!
The section provides an overview of polynomials in one variable, introducing key definitions, types, and properties, including degrees and coefficients.
This section discusses polynomials in one variable, detailing their components such as terms, coefficients, and degrees. It classifies polynomials based on the number of terms and their degrees, further explaining the significance of zeroes in polynomial equations. The section concludes by emphasizing the importance of polynomials in algebraic expressions and their applications.
In this section, we explore polynomials in one variable, defined as algebraic expressions of the form:
Where:
The expression is considered a polynomial if every term is of the form c * (variable) with whole number exponents. We categorize polynomials based on the number of terms:
The degree of a polynomial is the highest power of the variable present. For example, in the polynomial 4x^3 + 7x^2 - x + 1, the degree is 3. The section further highlights zeroes of polynomials, explaining that a zero of p(x) is a real number c such that p(c) = 0. The importance of the Factor Theorem and its application in identifying factors of polynomials based on their zeroes is also discussed, along with the use of polynomial equations in algebraic problem solving.