Algebra Class: Variables and Constants
25 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

Which of the following options correctly identifies the degree of the polynomial 13x⁴ + 4y⁷x?

  • 8
  • 4 (correct)
  • 11 (correct)
  • 7
  • The expression 2xy + 5y + 8 is a trinomial.

    True

    What is the coefficient of xy in the expression 4y12xy + 32?

    48

    The expression 3x + 4y + 2xy + 5x - xy - 2x simplifies to ___

    <p>6x + 3y + xy</p> Signup and view all the answers

    Match the following expressions with their classifications.

    <p>14abc + b = Binomial 3a5ab + 2c = Monomial 18pq = Monomial 5x + y = Binomial 2x - 5yz + 3z = Trinomial</p> Signup and view all the answers

    What is the result of multiplying 3ab by 2a?

    <p>6a²b</p> Signup and view all the answers

    The expansion of (a + 3)(a + 5) results in a² + 8a + 15.

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

    What is the product of (2x + 1)(x + 4)?

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

    The result of expanding (3x + 1)(2x + 5y + 6) is _____

    <p>6x² + 15xy + 18x + 2x + 6</p> Signup and view all the answers

    Match the expressions with their respective products:

    <p>(3x - 1)(x - 5) = 2x² - 8x + 5 (2a - 3)(3a + 4) = 6a² - 1 (4y - 1)(5y + 3) = 20y² - 27y - 3 (2z + 1)(z - 7) = 2z² - 13z - 7</p> Signup and view all the answers

    What is the expression for the distance travelled by the car in terms of x?

    <p>(70 - 3x)(x + 2)</p> Signup and view all the answers

    The area of the rectangular field is calculated by multiplying its length and width.

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

    If $x = 3$, what is the distance travelled by the car?

    <p>189 km</p> Signup and view all the answers

    The area of the rectangular field is ________ m² in terms of x.

    <p>(3x - 2)(x + 5)</p> Signup and view all the answers

    Match the following expressions with their operations:

    <p>(70 - 3x)(x + 2) = Distance travelled (3x - 2)(x + 5) = Area of rectangle (2x - 5)(3x + 7) = Coefficient of x x + 2 = Time taken by the car</p> Signup and view all the answers

    What is the result of dividing $12x^4$ by $3x^2$?

    <p>$4x^2$</p> Signup and view all the answers

    Dividing $39m^5$ by $13m^3$ results in $3m^2$.

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

    What is the remainder when dividing $7x^3 + 13x^2 - 16x + 23$ by $7x - 1$?

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

    The result of dividing $18x^2 + 12x$ by $6x$ is _____ .

    <p>3x + 2</p> Signup and view all the answers

    Match the following polynomials with their corresponding divisor:

    <p>$2x^3 + 19x^2 + 6x + 63$ = $x + 4$ $x^3 - 7x^2 + 10x$ = $x - 2$ $6x^6 - 3x^2 + 7x - 152$ = $x^2 - 3$ $x^4 + 4x^3 + 6x^2 + 2$ = $x + 1$</p> Signup and view all the answers

    What is the result of expanding (3m + 5n)²?

    <p>9m² + 30mn + 25n²</p> Signup and view all the answers

    (a + b)² = a² + 2ab + b² is a standard identity.

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

    What do you call a polynomial with two terms?

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

    The expression (x + 2)(x - 2) simplifies to __________.

    <p>x² - 4</p> Signup and view all the answers

    Match each polynomial type with its definition:

    <p>Monomial = A polynomial with one term Binomial = A polynomial with two terms Trinomial = A polynomial with three terms Polynomial = An algebraic expression with one or more terms</p> Signup and view all the answers

    Study Notes

    Variables and Constants

    • Variables are symbols representing unknown values, such as a, b, c, x, y, z, p.
    • Constants are fixed values in algebraic expressions, e.g., 8, 10, 5, 6.

    Types of Algebraic Expressions

    • Monomials: Expressions with one term, e.g., 3a5ab.
    • Binomials: Expressions with two terms, e.g., 14abc + b.
    • Trinomials: Expressions with three terms, e.g., 2x - 5yz + 3z.

    Coefficients

    • The coefficient is the numerical factor in a term, e.g., in 9xy, the coefficient is 9.

    Degree of Polynomials

    • The degree of a polynomial indicates the highest power of the variable, e.g., in 256z² + 8, the degree is 2.

    Addition and Subtraction of Expressions

    • Algebraic expressions can be combined through addition and subtraction by collecting like terms, e.g., 11a² + 2ab + 8 and 4ab + 6 simplifies to 11a² + 6ab + 14.

    Simplification Techniques

    • Collecting like terms helps simplify expressions, e.g., 3x + 4y + 2xy + 5x - xy - 2x reduces to 6x + 3y + xy.

    Multiplication of Algebraic Expressions

    • Use the distributive property to multiply terms, e.g., (a + b)(c + d) = ac + ad + bc + bd.

    Important Algebraic Identities

    • The square of a binomial: (a + b)² = a² + 2ab + b².
    • The difference of squares: (a + b)(a - b) = a² - b².

    Division of Polynomials

    • Dividing monomials involves subtracting exponents, e.g., x^m ÷ x^n = x^(m-n).
    • Polynomials can be divided by linear expressions, leading to a quotient and possibly a remainder.

    Problem Solving Techniques

    • For problem solving, setting up an expression based on given conditions helps in finding distances, areas, and solutions.

    Comparative Areas

    • To compare areas of shapes (e.g., square vs. rectangular window), calculate area using length and width and subtract to find the difference.

    Overview of Polynomials

    • A polynomial is an algebraic expression with non-negative integer exponents, categorized into monomials, binomials, and trinomials based on the number of terms.

    Studying That Suits You

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

    Quiz Team

    Description

    This quiz focuses on identifying variables and constants in various algebraic expressions. Participants will analyze different expressions and classify the components accurately. It serves as a valuable exercise for students in algebra to enhance their understanding of these fundamental concepts.

    More Like This

    Основные понятия алгебры
    10 questions
    Introduction to Algebra
    16 questions
    Use Quizgecko on...
    Browser
    Browser