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    Quarter 2 Module 5 Multiplication and Division of Polynomials2

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    charries vergara
    The document discusses laws of exponents for multiplication, division, and properties of exponents. It also covers multiplying and dividing polynomials using the distributive property and by grouping like terms. Examples are provided to illustrate multiplying terms with the same base, raising powers and products to powers, and dividing polynomials by monomials and other polynomials.

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    © All Rights Reserved
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    Quarter 2 Module 5 Multiplication and Division of Polynomials2

    Uploaded by

    charries vergara
    27 views41 pages
    The document discusses laws of exponents for multiplication, division, and properties of exponents. It also covers multiplying and dividing polynomials using the distributive property and by grouping like terms. Examples are provided to illustrate multiplying terms with the same base, raising powers and products to powers, and dividing polynomials by monomials and other polynomials.

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    Quarter-2-Module-5-Multiplication-and-Division-of-Polynomials2

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    The document discusses laws of exponents for multiplication, division, and properties of exponents. It also covers multiplying and dividing polynomials using the distributive property and by grouping like terms. Examples are provided to illustrate multiplying terms with the same base, raising powers and products to powers, and dividing polynomials by monomials and other polynomials.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    27 views41 pages

    Quarter 2 Module 5 Multiplication and Division of Polynomials2

    Uploaded by

    charries vergara
    The document discusses laws of exponents for multiplication, division, and properties of exponents. It also covers multiplying and dividing polynomials using the distributive property and by grouping like terms. Examples are provided to illustrate multiplying terms with the same base, raising powers and products to powers, and dividing polynomials by monomials and other polynomials.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 41

    PRAYER

    HANGING QUESTIONS:
    The length of a rectangle is 3x – 2.
    Its width is 2x.

    a. Find its area.

    b. Suppose x is 5 m, what is the


    area of the rectangle?
    THE LAWS OF EXPONENTS FOR
    MULTIPLICATION
    In multiplying polynomials
    using the distributive
    property, you will apply the
    laws of exponents for
    multiplication.
    THE LAWS OF EXPONENTS FOR
    MULTIPLICATION
    • Multiplying Powers with Like Bases

    For any real number a and for any


    positive integers m and n:

    • =
    • Multiplying Powers with
    Like Bases

    Examples:
    1. • = =
    2. • = =
    3. • = =
    THE LAWS OF EXPONENTS FOR
    MULTIPLICATION
    • Raising a Power to a Power

    For any real number a and for any


    positive integers m and n:

    n =
    • Raising a Power to a Power

    Examples:
    1. ()³ = = = 64
    2. ()³ = =
    3. ()² = =
    THE LAWS OF EXPONENTS FOR
    MULTIPLICATION
    • Raising a Product to a Power

    For any real number a and b and for any


    positive integer n:

    n
    (ab) = •
    • Raising a Product to a
    Power
    Examples:
    1. (4y)³ = =

    2. ()² ==

    3. (3)³ ==
    MULTIPLICATION OF
    POLYNOMIALS
    Multiplying Monomials
    Examples:
    1.5(3) =
    =
    MULTIPLICATION OF
    POLYNOMIALS
    Multiplying Monomials
    Examples:
    2. (8xy)(-2x) =
    =
    MULTIPLICATION OF POLYNOMIALS
    Multiplying Monomials
    Examples:
    3. (-5)³() = ) ()
    = ) ()
    =

    =
    Multiplying Two Binomials
    The process of multiplying binomials
    using the Distributive Property is better
    known as the FOIL method. The letters
    FOIL stand for F(first), O(outer), I(inner),
    and L(last). The word FOIL helps us
    remember which terms to multiply.
    Examples#1:
    Multiply (x + 4)(x + 3)

    F (x + 4)(x + 3) Multiply first terms: x²

    O (x + 4)(x + 3) Multiply outer terms: 3x

    I (x + 4)(x + 3) Multiply inner terms: 4x

    L (x + 4)(x + 3) Multiply last terms: 12


    x² + 3x + 4x + 12

    Answer:
    x² + 7x + 12
    Examples#2:
    Multiply (2x + 4)(x – 1)

    F (2x + 4)(x – 1) Multiply first terms: 2x²

    O (2x + 4)(x – 1) Multiply outer terms: -2x

    I (2x + 4)(x – 1) Multiply inner terms: 4x

    L (2x + 4)(x – 1) Multiply last terms: -4


    x² - 2x + 4x -4

    Answer:
    x² + 2x -4
    The Distributive Property can
    also be used to multiply
    polynomials of any number of
    terms
    Example:
    Multiply (3x + 2)(5x² – x – 4)
    Solution: Multiply each term of 3x + 2 to each terms of
    5x² – x – 4

    (3x + 2)(5x² – x – 4) = 3x(5x²) + 3x(-x) + 3x(-4)


    + 2(5x²) + 2(-x) + 2(-4)
    THE LAWS OF EXPONENTS FOR
    DIVISION
    • Quotient Rule
    For any nonzero real number a and for any integers m and
    n
    1. = if m n
    Examples:
    a. =
    = =8
    THE LAWS OF EXPONENTS FOR
    DIVISION
    • Quotient Rule
    For any nonzero real number a and for any integers m and
    n
    1. = if m n
    Examples:
    b. =
    𝟐𝟎 −𝟏𝟓
    𝒙 ¿𝒙 𝟓
    THE LAWS OF EXPONENTS FOR
    DIVISION
    • Definition of a Negative Exponent
    For any nonzero real number a and for
    any integer n.

    =
    THE LAWS OF EXPONENTS FOR
    DIVISION
    • Quotient Rule
    For any nonzero real number a and for any integers m and
    n
    2. = if m n
    Example:
    a. = = =
    THE LAWS OF EXPONENTS FOR
    DIVISION
    • Quotient Rule
    For any nonzero real number a and for any integers m and
    n
    3. = = 1 if m = n
    Examples:
    a. = = = 1
    b. = = = 1
    THE LAWS OF EXPONENTS FOR DIVISION
    • Raising a Quotient to a Power
    For any nonzero real number a and b, with b 0, and for any n.
    ()ᵑ =
    Example:

    a. ()³ =
    =
    DIVISION OF
    POLYNOMIALS
    Dividing Monomials
    If there are two or more variables in th
    base, treat the coefficient and each
    variable separately.
    Dividing Monomials
    Examples:
    a. = =
    Dividing Monomials
    Examples:

    (𝟒 −𝟒) (𝟕 −𝟐)
    b. = −𝟐𝐱 𝐳
    (𝟑 −𝟏)
    𝐲
    𝟓
    − 𝟐𝐳
    = 𝟐
    𝐲
    Dividing Monomials
    Examples:
    𝟒 (𝟑 −𝟐)
    c. = −𝟐𝒂 𝒃
    𝟓𝒄
    =
    Dividing a Polynomial by
    a Monomial
    To divide a polynomial by a
    monomial, we apply this
    property of fractions.
    = +
    Example:
    a. Divide by 8x
    Steps:
    1. Arrange the powers of a certain variable in
    descending order.
    2. Divide each term of the polynomial by the
    monomial.
    3. Add the resulting quotients.
    Solutions:
    == +
    + =
    +

    𝟐
    ¿𝟑𝐱 −𝟐 𝐱+𝟒
    Example:
    b. Divide by
    Steps:
    1. Arrange the powers of a certain variable in
    descending order.
    2. Divide each term of the polynomial by the
    monomial.
    3. Add the resulting quotients.
    Solutions:
    ==
    =

    =
    HANGING QUESTIONS:
    The length of a rectangle is 3x – 2.
    Its width is 2x.

    a. Find its area.

    b. Suppose x is 5 m, what is the


    area of the rectangle?
    HANGING QUESTIONS:
    Solutions:
    a. A = (L)(W) Area of a Rectangle

    A = (3x – 2)(2x)

    𝟐
    ¿𝟑𝐱 −𝟒𝒙
    HANGING QUESTIONS:
    Solutions: (3x – 2)(2x)

    b. If x = 5 m,
    3 (5) -2 = 15-2 =13 2(5) = 10

    13(10) = 130 m
    Asynchronous
    Direction: Show your
    solution in answering
    these activities.

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