Algebra 2 - Factoring Polynomials Flashcards
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Questions and Answers

What is a polynomial?

  • A variable
  • A monomial or the sum of monomials (correct)
  • A number
  • A product of a number and one variable

    • 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.

    <p>A number, a variable, or the product of a number and one or more variables.</p> Signup and view all the answers

    What is the standard form of a polynomial?

    <p>Has the terms in descending order by degree.</p> Signup and view all the answers

    What is a coefficient?

    <p>The numerical factor in a term.</p> Signup and view all the answers

    What is a binomial?

    <p>A polynomial with two terms.</p> Signup and view all the answers

    Define a trinomial.

    <p>A polynomial with three terms.</p> Signup and view all the answers

    What is a perfect square?

    <p>The product of a binomial squared</p> Signup and view all the answers

    What is a perfect cube?

    <p>The product that occurs when you cube a binomial.</p> Signup and view all the answers

    What does grouping refer to in polynomials?

    <p>When you have more than three terms and put alike terms together.</p> Signup and view all the answers

    Define the difference of squares.

    <p>The formula a^2 - b^2 = (a + b)(a - b).</p> Signup and view all the answers

    What is the sum of cubes formula?

    <p>(a + b)(a^2 - ab + b^2).</p> Signup and view all the answers

    Define the difference of cubes.

    <p>(a - b)(a^2 + ab + b^2).</p> Signup and view all the answers

    What is a quadratic equation?

    <p>ax^2 + bx + c = 0.</p> Signup and view all the answers

    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.

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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.

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