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
Multiplying Polynomials
2:01 minutes
Problem 15a
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. -7z^5-2z^3+1
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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 a mathematical expression consisting of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. Each term in a polynomial is formed by multiplying a coefficient (a constant) by a variable raised to a power. For example, -7z^5, -2z^3, and 1 are terms of a polynomial.
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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. It indicates the polynomial's behavior and the number of roots it can have. For instance, in the polynomial -7z^5 - 2z^3 + 1, the degree is 5, as the term with the highest exponent is -7z^5.
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Standard Form of Polynomials
Types of Polynomials
Polynomials can be classified based on the number of terms they contain. A monomial has one term, a binomial has two terms, and a trinomial has three terms. For example, -7z^5 is a monomial, while -7z^5 - 2z^3 + 1 is a trinomial, as it contains three distinct terms.
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