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    Factoring General Trinomials

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    OALICAN, JOHN NEIL E. 11-COOKERY1
    This document provides examples for factoring trinomials of the form Ax^2 + Bx + C. It outlines the steps to factor trinomials as follows: 1) Multiply the values of A and C to get the product. 2) Find two factors of the product whose sum is equal to B. 3) Replace B with the two factors. 4) Factor the trinomial using factoring by grouping. Several examples are worked through to demonstrate applying these steps to factor trinomial expressions.

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    Factoring General Trinomials

    Uploaded by

    OALICAN, JOHN NEIL E. 11-COOKERY1
    27 views24 pages
    This document provides examples for factoring trinomials of the form Ax^2 + Bx + C. It outlines the steps to factor trinomials as follows: 1) Multiply the values of A and C to get the product. 2) Find two factors of the product whose sum is equal to B. 3) Replace B with the two factors. 4) Factor the trinomial using factoring by grouping. Several examples are worked through to demonstrate applying these steps to factor trinomial expressions.

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    Factoring-General-Trinomials (1)

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    This document provides examples for factoring trinomials of the form Ax^2 + Bx + C. It outlines the steps to factor trinomials as follows: 1) Multiply the values of A and C to get the product. 2) Find two factors of the product whose sum is equal to B. 3) Replace B with the two factors. 4) Factor the trinomial using factoring by grouping. Several examples are worked through to demonstrate applying these steps to factor trinomial expressions.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    27 views24 pages

    Factoring General Trinomials

    Uploaded by

    OALICAN, JOHN NEIL E. 11-COOKERY1
    This document provides examples for factoring trinomials of the form Ax^2 + Bx + C. It outlines the steps to factor trinomials as follows: 1) Multiply the values of A and C to get the product. 2) Find two factors of the product whose sum is equal to B. 3) Replace B with the two factors. 4) Factor the trinomial using factoring by grouping. Several examples are worked through to demonstrate applying these steps to factor trinomial expressions.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 24

    Factoring General

    Quadratic Trinomial
    Lesson 4
    Factoring Trinomials of
    the Form
    Review: Find the product of (x + 3)(x + 2)
    using FOIL method.

    (x + 3) (x + 2)

    F - (x)(x) =
    2
    O - (x) (2) = 2x 𝑥 +5 𝑥 +6
    I - (3) (x) = 3x
    L - (3) (2) = 6
    Review: Find the product of (y + 6)(y – 2)
    using FOIL method.

    (y + 6)(y – 2)
    F - (y) (y) =
    2
    O - (y) (-2) = -2y 𝑦 + 4 𝑦 −12
    I - (6) (y) = 6y
    L - (6) (-2) = -12
    Trinomial - a polynomial with three terms.
    ,
    where B and C are real numbers and the
    coefficient of is 1.
    Listing Method
    List all the possible factors of the constant
    or the value of C.
    Examples: Determine the factors
    of the following.
    Example # 1: +7x + 6
    By Listing method:

    Factors of C Multiply the Add the Substitute Possible


    Factors Factors + Bx +C Factors
    (value of C) (value of B)

    1 and 6 6 7 + 7x + 6 (x + 1) (x +6)
    2 and 3 6 5 + 5x + 6 (x + 2) (x + 3)

    Thus + 7x + 6 = (x + 1) (x + 6)
    Example # 2:
    By Listing method:
    Factors of C Multiply the Add the Substitute Possible Factors
    Factors Factors + Bx +C
    (value of C) (value of B)

    -1 and -51 51 -52 - 52n +51 (n – 1) (n – 51)


    -3 and -17 51 -20 - 20n +51 (n – 3) (n – 17)

    Thus, = (n – 3) (n – 17)
    Example # 2:
    By Trial and Error:
    Factors whose product is 51 Sum of the Factors

    (-1)(-51) (-1) + (-51) = -52


    (-3)(-17) (-3) + (-17) = -20
    Thus, = (n – 3) (n – 17)
    Example # 3:
    By Listing method:
    Factors of C Multiply the Add the Substitute Possible
    Factors Factors + Bx +C Factors
    (value of C) (value of B)

    -1 and 6 -6 5 + 5p – 6 (p – 1) (p + 6)
    -2 and 3 -6 1 +p–6 (p – 2) (p + 3)

    Thus, = (p – 2) (p + 3)
    Example # 3:
    By Trial and Error:
    Factors whose product is -6 Sum of the Factors

    (-1)(6) (-1) + 6 = 5
    (-2)(3) (-2) + 3 = 1
    Thus, = (p – 2) (p + 3)
    Factoring trinomials of the
    form Ax² + Bx + C
    Review: Find the factors of the following

    a. a²+ 3a + 2 b. b ² – b – 6
    (a + ) (a + ) (b – ) (b + )
    (a + 2) (a + 1 ) (b – 3 ) (b + 2 )
    Review: Find the factors of the following

    c. m²+ 16m + 39 d. x ²+ 3x – 28

    (m + ) (m + ) (x – ) (x + )
    (m + 3 ) (m +13) (x – 4 ) (x + 7 )
    Factoring trinomials of the form
    Ax² + Bx + C
    Where A, B, and C are real numbers.
    Identify the A, B, and C.

    3x² + 5x + 2
    A=3, B=5, C=2

    8x² - 14x + 3
    A=8, B=-14, C=3
    Steps in Factoring Trinomials of the Form Ax² + Bx + C.

    a. Multiply the value of A and C.


    b. Factor the product of A and C such that those factors
    will have the sum equal to B.
    c. Replace B with a + b.
    d. Perform factoring by grouping.
    Examples: Determine the factors
    of the following.
    Example #1: 6x² + 17x + 5
    a. (6)(5) = 30
    b. 15 and 2 = 15 + 2 = 17
    c. 6x² + 17x + 5 = 6x² +(15x + 2x) + 5
    d. 6x² +(15x + 2x) + 5 = (6x² + 2x) (15x + 5)
    2x(3x + 1) + 5(3x + 1)= (3x + 1) (2x + 5)
    Example #2: 2x² + 7x + 3
    a. (2)(3) = 6

    b. 6 and 1 = 6 + 1 = 7
    c. 2x² + 7x + 3 = 2x² +(6x + x) + 3
    d. 2x² +(6x + x) + 3 = (2x² + 6x) (x + 3)

    2x(x + 3) + (x + 3)= (x + 3) (2x + 1)


    Example #3: 4c² - 6c + 2
    a. (4)(2) = 8
    b. -2 and -4 = -2 + (-4) = -6
    c. 4c² - 6c + 2 = 4c² +(-2c – 4c) + 2
    d. 4c² +(-2c – 4c) + 2 = (4c² - 2c) (-4c + 2)
    2c(2c - 1) - 2(2c - 1)= (2c - 1) (2c - 2)
    Example #4: 15n² - 2n – 1
    a. (15)(-1) = -15
    b. 3 and -5 = 3 + (-5) = -2
    c. 15n² - 2n – 1 = 15n² +(3n – 5n) – 1
    d. 15n² + (3n – 5n) – 1= (15n² - 5n) (3n – 1)
    5n(3n - 1) + (3n – 1)= (3n – 1) (5n + 1)
    QUESTIONS?
    THANK YOU!

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