Algebra: Polynomials and Their Degrees
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Questions and Answers

What is a monomial?

  • An expression with two terms.
  • An expression with multiple coefficients.
  • An expression with three terms. (correct)
  • An expression with one term. (correct)

    • Which of the following correctly defines a binomial?

  • An expression with three terms.
  • An expression with no terms.
  • An expression that has one term.
  • An expression that has two terms. (correct)

    • What characterizes a trinomial?

  • It is an expression with two variables.
  • It is an expression with only one variable.
  • It has three terms. (correct)
  • It contains only coefficients.

    • What does the term 'polynomial' refer to?

    <p>An expression made up of variables and coefficients.</p> Signup and view all the answers

    In the expression 38m, what is 38 considered?

    <p>A coefficient.</p> Signup and view all the answers

    What is an expression in mathematics?

    <p>A mathematical phrase containing numbers, variables, and operators.</p> Signup and view all the answers

    Which of the following is NOT a term in the expression 7a² - $ rac{3}{5}ab + 6b²?

    <p>4a + b</p> Signup and view all the answers

    How many terms are in the expression 3x + 9?

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

    Which of the following correctly identifies a term in the expression -7y + $ rac{1}{2}$?

    <p>-7y</p> Signup and view all the answers

    Which of the following is an example of an expression?

    <p>3x + 9</p> Signup and view all the answers

    What is the degree of the polynomial -3x² + 4x + 7?

    <p>2</p> Signup and view all the answers

    Which term represents a constant in the expression 8x - 4 + 3y?

    <p>-4</p> Signup and view all the answers

    What is the standard form of the expression 5 + 2x³ - x?

    <p>2x³ - x + 5</p> Signup and view all the answers

    How do you identify the degree of the polynomial 10y⁴ - y + 6?

    <p>By locating the term with the largest exponent</p> Signup and view all the answers

    What is the degree of the constant 0.5 in polynomial terms?

    <p>0</p> Signup and view all the answers

    What is the degree of the monomial $7a^2$?

    <p>2</p> Signup and view all the answers

    Calculate the degree of the monomial $1.79x^3y^2$.

    <p>5</p> Signup and view all the answers

    What is the degree of the monomial $\frac{3}{5}abc^2$?

    <p>7</p> Signup and view all the answers

    What is the implied exponent of a variable without a written exponent in a monomial?

    <p>1</p> Signup and view all the answers

    Which of the following expressions has the highest degree?

    <p>$5y^3$</p> Signup and view all the answers

    What is the first term written when rewriting the given polynomial expression in standard form?

    <p>(2/9)a²bc⁸</p> Signup and view all the answers

    Which variable comes first when arranging the polynomial terms in alphabetical order?

    <p>a</p> Signup and view all the answers

    In the final standard form, what is the coefficient of the term 4a³b²c⁵?

    <p>4</p> Signup and view all the answers

    What is the last term written in the standard form of the polynomial?

    <p>7abc²</p> Signup and view all the answers

    What is the highest power of 'a' in the expression before rewriting it in standard form?

    <p>3</p> Signup and view all the answers

    What is the first step in rewriting the polynomial 9x² - 4x + 5/2 + 10x³ in standard form?

    <p>Identify the term with the highest exponent</p> Signup and view all the answers

    How should terms be arranged in a polynomial with two variables, such as 7x³y⁵ - 8x²y²?

    <p>First alphabetically by variable, then in descending order of exponents for the leading variable</p> Signup and view all the answers

    In the standard form of a polynomial, what should be done with the signs of the terms?

    <p>Maintain the original signs of the terms</p> Signup and view all the answers

    For the polynomial expression 10x³ + 9x² - 4x + 5/2, what is the correct standard form arrangement?

    <p>10x³ + 9x² - 4x + 5/2</p> Signup and view all the answers

    In which order should the terms in a polynomial be organized when rewriting it?

    <p>First by alphabetically and then in descending order of the leading variable's exponents</p> Signup and view all the answers

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