Algebra 1 | Polynomials Flashcards
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Algebra 1 | Polynomials Flashcards

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Questions and Answers

What is a polynomial?

  • An algebraic expression containing 1 or more terms (correct)
  • A visual representation of data
  • A mathematical constant
  • A type of equation with no variables
  • What is a monomial?

    An expression that can be written as a real number, a variable, or a product of a real number and one or more variables with non-negative powers.

    What is a binomial?

    A polynomial with two terms.

    What is a trinomial?

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

    What is an expression?

    <p>A group of symbols that make a mathematical statement.</p> Signup and view all the answers

    What is the degree of a polynomial?

    <p>The exponent of the highest power of that variable.</p> Signup and view all the answers

    What is the greatest common factor?

    <p>The largest factor that two or more numbers have in common.</p> Signup and view all the answers

    What does distributing mean in algebra?

    <p>To multiply out of the parenthesis with the terms in the parenthesis.</p> Signup and view all the answers

    What is the difference of two squares?

    <p>Two perfect squares separated by a subtraction sign.</p> Signup and view all the answers

    What is a perfect-square trinomial?

    <p>The product obtained when you square a binomial.</p> Signup and view all the answers

    What is the degree of a monomial?

    <p>The sum of the exponents of the variables in the monomial.</p> Signup and view all the answers

    What is the standard form of a polynomial?

    <p>The degrees of its monomial terms decrease from left to right.</p> Signup and view all the answers

    What is a perfect square?

    <p>A number whose positive square root is a whole number.</p> Signup and view all the answers

    What is the degree of a term?

    <p>The sum of the exponents of the variables in the term.</p> Signup and view all the answers

    What is area?

    <p>Area of a 3-D object and how much space it takes up.</p> Signup and view all the answers

    What does it mean to factor a polynomial?

    <p>To write a polynomial as the product of monomial factors and prime factors with at least two terms.</p> Signup and view all the answers

    What does factoring mean?

    <p>To break down an expression into simpler components.</p> Signup and view all the answers

    How does a trinomial work?

    <p>A trinomial usually consists of three terms, one of which is often squared.</p> Signup and view all the answers

    What does a standard form look like?

    <p>A standard form of any polynomial looks like $4^2 + 24x + 12$.</p> Signup and view all the answers

    What are factors?

    <p>The numbers used to break down a bigger number.</p> Signup and view all the answers

    Study Notes

    Polynomials

    • An algebraic expression composed of one or more terms, categorized as monomials, binomials, or trinomials.

    Monomials

    • Defined as expressions that can be a real number, variable, or a product of a real number and variables with nonnegative powers.

    Binomials

    • A specific type of polynomial that consists of exactly two terms.

    Trinomials

    • A polynomial that includes three distinct terms.

    Expression

    • Represents a collection of symbols that form a mathematical statement, such as 8 + 7.

    Degree of Polynomial

    • Refers to the exponent of the highest power present among its variables.

    Greatest Common Factor (GCF)

    • The largest factor that two or more numbers share in common, essential for simplifying expressions.

    Distributing

    • The process of multiplying a term outside the parentheses with each term inside the parentheses.

    Difference of Two Squares

    • Represents two perfect squares separated by a minus sign, expressed as a² - b² = (a+b)(a-b).

    Perfect-Square Trinomial

    • Formed by squaring a binomial, resulting in a trinomial of the format a² + 2ab + b² or a² - 2ab + b².

    Degree of Monomial

    • Calculated as the sum of the exponents of all variables within that monomial.

    Standard Form of a Polynomial

    • Arranged such that the degrees of its monomial terms decrease sequentially from left to right.

    Perfect Square

    • A number whose positive square root is a whole number, e.g., 1, 4, 9, 16.

    Degree of Term

    • Determined by summing the exponents of all variables in a specific term.

    Area

    • The measurement of space within a 3D object, calculated as A = length x width x height.

    Factor a Polynomial

    • A polynomial is in factored form if expressed as a product of monomial factors and prime factors, requiring at least two terms.

    Factoring

    • The process of breaking an expression down into simpler components, such as turning 6x² + 2x + 21x + 7 into (2x + 7)(3x + 1) after extracting the GCF.

    How a Trinomial Works

    • Typically comprises three terms, with one squared, plus one variable term, formulated by adding/subtracting others (e.g., a² + 3m + 4).

    How Standard Form Looks

    • A polynomial in standard form is arranged as follows: 4x² + 24x + 12.

    Factors

    • Essential components used to decompose a larger number into parts that divide evenly into it.

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    Description

    Test your understanding of polynomials with these flashcards designed for Algebra 1. Each card presents a key term related to polynomials, including definitions of monomials, binomials, and trinomials. Brush up on your algebra vocabulary and enhance your skills!

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