Questions and Answers
What is a polynomial?
What is the greatest common factor (GCF)?
The common factor with the greatest coefficient and the greatest exponent.
What does the degree of a polynomial refer to?
The exponent of the variable in a term.
Define a term in polynomials.
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What is the standard form of a polynomial?
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What is a coefficient?
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What is a binomial?
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Define a trinomial.
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What is a perfect square?
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What is a perfect cube?
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What does grouping refer to in polynomials?
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Define the difference of squares.
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What is the sum of cubes formula?
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Define the difference of cubes.
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What is a quadratic equation?
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Study Notes
Polynomials and Their Components
- A polynomial can be defined as a monomial or the sum of multiple monomials.
- The Greatest Common Factor (GCF) is the highest common factor that shares the greatest coefficient and highest exponent among the terms.
- The degree refers to the highest exponent present in a term of a polynomial.
- A term may consist of a single number, a variable, or a product of a number with one or more variables.
Polynomial Form and Structure
- Standard form of a polynomial is achieved when its terms are arranged in descending order based on their degree.
- A coefficient represents the numerical factor associated with a term in a polynomial.
Types of Polynomials
- A binomial is categorized as having two terms.
- A trinomial consists of three terms and can be expressed in specific factored forms such as (a^2 + 2ab + b^2 = (a+b)^2) or (a^2 - 2ab + b^2 = (a-b)^2).
Special Products
- A perfect square is the product obtained when squaring a binomial.
- A perfect cube results from cubing a binomial or using the formula for the sum or difference of cubes.
Factoring Techniques
- Grouping is applicable when a polynomial has more than three terms where similar terms can be combined for simplification.
- The difference of squares formula is given by (a^2 - b^2 = (a+b)(a-b)), facilitating the factoring of specific polynomial types.
- The sum of cubes can be factored using the formula ((a+b)(a^2 - ab + b^2)).
- The difference of cubes has the factoring form ((a-b)(a^2 + ab + b^2)).
Quadratic Equations
- A standard quadratic equation is presented in the form (ax^2 + bx + c = 0) and represents a polynomial of degree two.
Studying That Suits You
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Test your knowledge of factoring polynomials with these flashcards. Each card features a key term related to polynomials, along with its definition. Perfect for reinforcing your understanding of algebraic concepts.
