Podcast
Questions and Answers
What is a monomial?
What is a monomial?
- A sum of monomials
- A polynomial with exactly 2 terms
- A real number or a variable (correct)
- A polynomial with exactly 3 terms
What defines a polynomial?
What defines a polynomial?
A monomial or a sum of monomials
What is a term in polynomials?
What is a term in polynomials?
Each monomial part of a polynomial
How many terms does a binomial have?
How many terms does a binomial have?
How many terms does a trinomial have?
How many terms does a trinomial have?
What is the degree of a monomial?
What is the degree of a monomial?
What determines the degree of a polynomial?
What determines the degree of a polynomial?
What is the standard form of a polynomial?
What is the standard form of a polynomial?
A polynomial of degree 0 (like -17) has no variable and is called a ______.
A polynomial of degree 0 (like -17) has no variable and is called a ______.
A polynomial of degree 1 (like 5x + 3) is called ______.
A polynomial of degree 1 (like 5x + 3) is called ______.
A polynomial of degree 3 (like 4r^3 + 5r^2) is called ______.
A polynomial of degree 3 (like 4r^3 + 5r^2) is called ______.
Any degree larger than 3 is named by its ______ ________.
Any degree larger than 3 is named by its ______ ________.
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Study Notes
Key Concepts in Polynomials
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Monomial: Defined as a real number, a variable, or the product of a real number and one or more variables raised to whole number exponents.
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Polynomial: Represents either a single monomial or a sum of multiple monomials, forming a broader category of mathematical expressions.
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Term: Refers specifically to each individual monomial component within a polynomial.
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Binomial: A specific type of polynomial characterized by having exactly two distinct terms.
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Trinomial: A polynomial that consists of exactly three separate terms.
Degree of Polynomials
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Degree of a Monomial: Calculated as the sum of the exponents of its variables. For constants (nonzero values), the degree is 0. The number zero itself is considered to have no degree.
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Degree of a Polynomial: Identified as the highest degree of any individual term within the polynomial.
Standard Form and Classification
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Standard Form of a Polynomial: The arrangement of its terms requires that the degrees are ordered in descending order from left to right.
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Constant Polynomial: A polynomial with a degree of 0; it does not involve any variables (e.g., -17).
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Linear Polynomial: A polynomial that has a degree of 1, exemplified by expressions like 5x + 3.
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Cubic Polynomial: A polynomial featuring a degree of 3, illustrated by terms such as 4r^3 + 5r^2.
Higher Degrees
- Degree Naming: Polynomials that have degrees larger than 3 are referred to by their degree. For example, a polynomial such as 18x^4 - 9x^3 + 2x is termed a "fourth degree polynomial" due to its highest degree of 4.
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