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    8-5 Study Guide and Intervention: Using The Distributive Property

    Uploaded by

    Diana Solano
    This document provides examples and exercises on using the distributive property to factor polynomials and solve equations. It shows how to factor polynomials by finding the greatest common factor and writing each term as a product of the GCF and remaining factors. It also demonstrates using the zero product property and factoring to solve equations of the form ab = 0. Students are given 18 exercises to factor polynomials and solve equations by applying these concepts.

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    8-5 Study Guide and Intervention: Using The Distributive Property

    Uploaded by

    Diana Solano
    761 views3 pages
    This document provides examples and exercises on using the distributive property to factor polynomials and solve equations. It shows how to factor polynomials by finding the greatest common factor and writing each term as a product of the GCF and remaining factors. It also demonstrates using the zero product property and factoring to solve equations of the form ab = 0. Students are given 18 exercises to factor polynomials and solve equations by applying these concepts.

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    This document provides examples and exercises on using the distributive property to factor polynomials and solve equations. It shows how to factor polynomials by finding the greatest common factor and writing each term as a product of the GCF and remaining factors. It also demonstrates using the zero product property and factoring to solve equations of the form ab = 0. Students are given 18 exercises to factor polynomials and solve equations by applying these concepts.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    761 views3 pages

    8-5 Study Guide and Intervention: Using The Distributive Property

    Uploaded by

    Diana Solano
    This document provides examples and exercises on using the distributive property to factor polynomials and solve equations. It shows how to factor polynomials by finding the greatest common factor and writing each term as a product of the GCF and remaining factors. It also demonstrates using the zero product property and factoring to solve equations of the form ab = 0. Students are given 18 exercises to factor polynomials and solve equations by applying these concepts.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
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    The passage discusses using the distributive property to factor polynomials and solve equations.

    The distributive property allows you to multiply a polynomial by a monomial. It can be used to express a polynomial in factored form by finding the GCF.

    To factor a polynomial using the GCF, you find the largest term that divides each term and group the remaining factors.

    NAME ______________________________________________ DATE______________________________ PERIOD ______________

    8-5 Study Guide and Intervention


    Using the Distributive Property
    Use the Distributive Property to Factor The Distributive Property has been used to multiply a polynomial by a
    monomial. It can also be used to express a polynomial in factored form. Compare the two columns in the table below.
    Multiplying Factoring
    3(a + b) = 3a + 3b 3a + 3b = 3(a + b)
    x(y – z) = xy – xz xy – xz = x(y – z)
    6y(2x + 1) = 6y(2x) + 6y(1) 12xy + 6y = 6y(2x) + 6y(1)
    = 12xy + 6y = 6y(2x + 1)

    Example 1: Use the Distributive Property to Thus 12mp + 80m 2 = 4m(3p + 20m).
    factor 12mp + 80m 2.
    Example 2: Factor 6ax + 3ay + 2bx + by
    2 by grouping.
    Find the GCF of 12mp and 80m .
    12mp = 2 ⋅ 2 ⋅ 3 ⋅ m ⋅ p 6ax + 3ay + 2bx + by

    80m 2 = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ m ⋅ m = (6ax + 3ay) + (2bx + by)

    GCF = 2 ⋅ 2 ⋅ m or 4m = 3a(2x + y) + b(2x + y)

    Write each term as the product of the GCF and its = (3a + b)(2x + y)
    remaining factors. Check using the FOIL method.
    2
    12mp + 80m = 4m(3 ⋅ p) + 4m(2 ⋅ 2 ⋅ 5 ⋅ m) (3a + b)(2x + y)
    = 4m(3p) + 4m(20m) = 3a(2x) + (3a)(y) + (b)(2x) + (b)(y)
    = 4m(3p + 20m) = 6ax + 3ay + 2bx + by 

    Exercises
    Factor each polynomial.
    1. 24x + 48y 2. 30m p2 + m 2p – 6p 3. q 4 – 18q 3 + 22q

    4. 9 x 2 – 3x 5. 4m + 6p – 8mp 6. 45r 3 – 15r 2

    7. 14t 3 – 42t 5 – 49t 4 8. 55 p2 – 11 p4 + 44 p5 9. 14 y 3 – 28 y 2 + y

    10. 4x + 12 x 2 + 16 x 3 11. 4a 2b + 28ab 2 + 7ab 12. 6y + 12x – 8z

    13. x 2 + 2x + x + 2 14. 6 y 2 – 4y + 3y – 2 15. 4m 2 + 4mp + 3mp + 3 p2

    16. 12ax + 3xz + 4ay + yz 17. 12a 2 + 3a – 8a – 2 18. xa + ya + x + y

    Chapter 8 31 Glencoe Algebra 1


    NAME ______________________________________________ DATE______________________________ PERIOD ______________

    8-5 Study Guide and Intervention (continued)


    Using the Distributive Property
    Solve Equations by Factoring The following property, along with factoring, can be used to solve certain equations.

    Zero Product Property For any real numbers a and b, if ab = 0, then either a = 0, b = 0, or both a and b equal 0.

    Example : Solve 9 x 2 + x = 0. Then check the solutions.


    Write the equation so that it is of the form ab = 0.
    9x2 + x = 0 Original equation
    2
    x(9x + 1) = 0 Factor the GCF of 9 x + x, which is x.

    x = 0 or 9x + 1 = 0 Zero Product Property

    1
    x=0 x=– Solve each equation.
    9
    1
    Check Substitute 0 and – for x in the original equation.
    9
    9x2 + x = 0 9x2 + x = 0

    −1 2 −1
    9( 0 )2 + 0 ≟ 0 9 ( ) ( )
    9
    +
    9
    ≟0

    1 −1
    9 ( 9 )
    0=0 + ≟0

    0=0
    1
    The solution set is 0 ,−{ 9 }
    .

    Exercises
    Solve each equation. Check your solutions.
    1. x(x + 3) = 0 2. 3m(m – 4) = 0 3. (r – 3)(r + 2) = 0

    4. 3x(2x – 1) = 0 5. (4m + 8)(m – 3) = 0 6. 5t 2 = 25t

    7. (4c + 2)(2c – 7) = 0 8. 5p – 15 p2 = 0 9. 4 y 2 = 28y

    10. 12 x 2 = –6x 11. (4a + 3)(8a + 7) = 0 12. 8y = 12 y 2

    13. x 2 = –2x 14. (6y – 4)(y + 3) = 0 15. 4m 2 = 4m

    Chapter 8 32 Glencoe Algebra 1


    NAME ______________________________________________ DATE______________________________ PERIOD ______________

    16. 12x = 3 x 2 17. 12a 2 = –3a 18. (12a + 4)(3a – 1) = 0

    Chapter 8 32 Glencoe Algebra 1

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