Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Polynomials Intro
2:31 minutes
Problem 17b
Textbook Question
Textbook QuestionIdentify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. 15a^2b^3+12a^3b^8-13b^5+12b^6
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Definition
A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients. It can include constants and can be expressed in the form of a sum of terms, where each term is a product of a coefficient and a variable raised to a power. Expressions that contain negative exponents, fractional exponents, or variables in the denominator are not considered polynomials.
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Introduction to Polynomials
Degree of a Polynomial
The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 3x^4 + 2x^2 + 1, the degree is 4 because the term with the highest exponent is x^4. The degree helps classify the polynomial and is crucial for understanding its behavior and graphing.
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Types of Polynomials
Polynomials can be classified based on the number of terms they contain. A monomial has one term (e.g., 5x), a binomial has two terms (e.g., x + 3), and a trinomial has three terms (e.g., x^2 + 2x + 1). If a polynomial has more than three terms, it is simply referred to as a polynomial without a specific name. This classification aids in identifying the structure of the polynomial.
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