Polynomials Basics
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Questions and Answers

What is the definition of a polynomial?

  • An expression consisting of variables and coefficients combined using only addition and subtraction.
  • An expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. (correct)
  • An expression consisting of variables and coefficients combined using only exponentiation and logarithms.
  • An expression consisting of variables and coefficients combined using only multiplication and division.

    • What is the degree of a polynomial?

  • The highest power of the variable in a polynomial. (correct)
  • The product of the powers of the variables in a polynomial.
  • The lowest power of the variable in a polynomial.
  • The sum of the powers of the variables in a polynomial.

    • What is a monomial?

  • A polynomial with two terms.
  • A polynomial with any number of terms.
  • A polynomial with only one term. (correct)
  • A polynomial with three terms.

    • What is the distributive property of polynomials?

    <p>A polynomial can be distributed over addition or subtraction.</p> Signup and view all the answers

    What is the greatest common factor (GCF) of two polynomials?

    <p>The largest polynomial that divides both polynomials.</p> Signup and view all the answers

    What happens when you add or subtract polynomials?

    <p>You combine like terms by adding or subtracting their coefficients.</p> Signup and view all the answers

    Study Notes

    Definition

    A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.

    Characteristics

    • A polynomial can have any number of terms, but it cannot have variables in the denominator.
    • The variables in a polynomial are raised to non-negative integer powers.
    • Coefficients can be any real numbers, including fractions and decimals.

    Types of Polynomials

    • Monomial: A polynomial with only one term.
    • Binomial: A polynomial with two terms.
    • Trinomial: A polynomial with three terms.

    Operations with Polynomials

    • Addition and Subtraction: Combine like terms by adding or subtracting their coefficients.
    • Multiplication: Multiply each term in one polynomial by each term in the other polynomial, then combine like terms.

    Properties of Polynomials

    • Commutative Property: The order of the terms in a polynomial does not change its value.
    • Associative Property: The order in which polynomials are added or multiplied does not change the result.
    • Distributive Property: A polynomial can be distributed over addition or subtraction.

    Factors of Polynomials

    • Greatest Common Factor (GCF): The largest polynomial that divides two or more polynomials.
    • Factoring Out the GCF: Divide each term of a polynomial by the GCF to simplify the expression.

    Important Concepts

    • Degree of a Polynomial: The highest power of the variable in a polynomial.
    • Leading Coefficient: The coefficient of the term with the highest power of the variable.
    • Roots of a Polynomial: The values of the variable that make the polynomial equal to zero.

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    Description

    Learn about the definition, characteristics, and types of polynomials, as well as operations, properties, and factors of polynomials. Understand important concepts like degree, leading coefficient, and roots of a polynomial.

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