Algebra Basics: Real Numbers and Polynomials
7 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What can be said about the decimal form of a real number?

  • It always terminates
  • It always repeats
  • It may terminate or repeat (correct)
  • It is always an integer

    • What is the degree of the polynomial 2x^3 - 5x^2 + x?

  • 4
  • 2
  • 1
  • 3 (correct)

    • Which of the following is a binomial?

  • x^2 + 3x - 2
  • 2x^3 - 5x^2 + x
  • x + 2 (correct)
  • 3x

    • What is the property of polynomial operations that states a + b = b + a?

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

    What is the result of combining like terms in polynomial addition and subtraction?

    <p>The like terms are added or subtracted</p> Signup and view all the answers

    What is the expression of a polynomial in general form?

    <p>a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0</p> Signup and view all the answers

    What is the result of multiplying two polynomials?

    <p>A polynomial with a degree equal to the sum of the degrees of the original polynomials</p> Signup and view all the answers

    Study Notes

    Real Numbers

    • A real number is a value that can be represented on the number line
    • Can be expressed in decimal form, which may terminate or repeat
    • Includes:
      • Natural numbers (1, 2, 3, ...)
      • Whole numbers (0, 1, 2, ...)
      • Integers (...,-2, -1, 0, 1, 2, ...)
      • Rational numbers (fractions, e.g., 3/4, 22/7)
      • Irrational numbers (non-repeating, non-terminating decimals, e.g., π, e)

    Polynomials

    • A polynomial is an expression consisting of variables (e.g., x, y) and coefficients (numbers)
    • Form: a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0
    • Where:
      • a_n is the leading coefficient
      • x is the variable
      • n is the degree of the polynomial (highest power of x)
    • Examples:
      • Monomials: 3x, 2y^2
      • Binomials: x + 2, 3x^2 - 4x
      • Trinomials: x^2 + 3x - 2, 2x^3 - 5x^2 + x

    Operations with Polynomials

    • Addition and subtraction:
      • Combine like terms (terms with the same variable and exponent)
    • Multiplication:
      • Distribute each term in one polynomial to each term in the other
    • Properties:
      • Commutative: a + b = b + a and a × b = b × a
      • Associative: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)
      • Distributive: a × (b + c) = a × b + a × c

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    Test your knowledge of real numbers and polynomials, including their definitions, properties, and operations. Learn about the different types of real numbers and how to add, subtract, and multiply polynomials.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser