Polynomial Vocabulary Study Notes
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Questions and Answers

What are terms in a polynomial separated by?

  • Multiplication
  • Division
  • Exponentiation
  • Plus or minus (correct)

    • What are factors?

    Numbers or expressions that multiply together.

    Define monomial.

    One term.

    What is a binomial?

    <p>Two terms.</p> Signup and view all the answers

    Define polynomial.

    <p>The sum or difference of multiple terms with positive integer exponents.</p> Signup and view all the answers

    What is the leading coefficient?

    <p>The number in front of the term with the highest degree.</p> Signup and view all the answers

    What is a constant term?

    <p>The term without a variable.</p> Signup and view all the answers

    What represents the degree of the polynomial?

    <p>The largest degree (exponent).</p> Signup and view all the answers

    What is standard form?

    <p>When all the terms are written in order from largest exponent to smallest exponent.</p> Signup and view all the answers

    Define trinomial.

    <p>Three terms.</p> Signup and view all the answers

    What is a quadratic function's degree?

    <ol start="2"> <li></li> </ol> Signup and view all the answers

    What is a cubic function's degree?

    <ol start="3"> <li></li> </ol> Signup and view all the answers

    What are zeros in a polynomial?

    <p>Real solutions for an equation, also known as x-intercepts.</p> Signup and view all the answers

    What degree does a quartic function have?

    <ol start="4"> <li></li> </ol> Signup and view all the answers

    What are roots?

    <p>Solutions for an equation (can be imaginary).</p> Signup and view all the answers

    What defines the end behavior of a polynomial function?

    <p>The behavior of the graph as x approaches positive or negative infinity.</p> Signup and view all the answers

    What are turning points?

    <p>When the function changes from increasing to decreasing or vice versa.</p> Signup and view all the answers

    Flashcards

    Polynomial Terms Separator

    Terms in a polynomial are separated by plus (+) or minus (-) signs.

    Factors

    Numbers or expressions that are multiplied together.

    Monomial

    A polynomial with one term.

    Binomial

    A polynomial with two terms.

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    Polynomial

    A sum or difference of multiple terms with positive integer exponents.

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    Leading Coefficient

    The number before the term with the highest exponent.

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    Constant Term

    The term without a variable.

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    Polynomial Degree

    The largest exponent (power) in the polynomial.

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    Standard Form

    Polynomial written with terms ordered from highest to lowest exponent.

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    Trinomial

    A polynomial with three terms.

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    Quadratic Function Degree

    Degree of 2.

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    Cubic Function Degree

    Degree of 3.

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    Polynomial Zeros

    Real solutions to the polynomial equation when set to zero.

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    Quartic Function Degree

    Degree of 4.

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    Polynomial Roots

    Solutions of a polynomial equation (can be real or imaginary).

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    End Behavior

    How the graph of a polynomial behaves as x goes to positive or negative infinity.

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    Turning Points

    Where a function changes from increasing to decreasing or vice versa.

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    Study Notes

    Polynomial Vocabulary Study Notes

    • Term: Represents individual components in a polynomial, separated by plus or minus signs.
    • Factor: Elements that multiply to produce a number or expression; a factor divides its corresponding number without a remainder.
    • Monomial: A polynomial consisting of only one term.
    • Binomial: A polynomial composed of two distinct terms.
    • Polynomial: An expression formed by summing or subtracting multiple terms, where each term contains variables raised to positive integer exponents.
    • Leading Coefficient: The coefficient of the term with the highest degree within a polynomial, indicating its growth rate.
    • Constant Term: The term that remains after variables are eliminated, essentially a standalone number.
    • Degree of the Polynomial: Identifies the highest exponent in the polynomial, indicating its overall degree.
    • Standard Form: A format where polynomial terms are organized from highest to lowest exponent, providing clarity on the polynomial's degree.
    • Trinomial: A polynomial made up of three separate terms.
    • Quadratic: Refers to polynomials (or functions) that have a degree of 2, typically resulting in a parabolic graph.
    • Cubic: Denotes polynomials with a degree of 3, producing S-shaped graphs.
    • Zeros: Real solutions to a polynomial equation; also defined as the x-intercepts of its graph.
    • Quartic: A polynomial function characterized by a degree of 4, exhibiting complex curves.
    • Roots: Solutions for polynomial equations, which may include both real and imaginary numbers.
    • End Behavior: Describes the trend of a polynomial's graph as the input value approaches positive or negative infinity, indicating how the graph behaves in extreme values.
    • Turning Points: Points on the graph where the polynomial function transitions between increasing and decreasing; can represent hills or valleys in the graph.

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    Description

    This quiz focuses on key vocabulary related to polynomials, essential for understanding algebraic expressions. Explore important terms like monomial, binomial, leading coefficient, and more to enhance your grasp of polynomial concepts. Perfect for students studying algebra and polynomial functions.

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