Examples Factor the followings by grouping 1 3xx y 2x y 2 3x 2 x y 6xx y 9x y 3

Examples factor the followings by grouping 1 3xx y 2x

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Examples: Factor the followings by grouping. 1. 3x(x + y) + 2(x + y) 2. 3x 2 (x y) + 6x(x y) + 9(x y) 3. ax ay + bx by 4. 2x 3 + 3x 2 6x + 9 5. x 2 6yz + 2xy 3xz 8
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5.2: Factoring Special Polynomials Objectives: 5.2.1: Factor the difference of squares 5.2.2: Factor the sum and difference of cubes 9
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5.2.1: Factor the Difference of Squares The product of a sum and difference of two terms such as (a + b)(a b) = a 2 b 2 This also means that a binomial of the form a 2 b 2 is called the difference of squares, and its factors a + b and a b Examples: Factor the followings 1. x 2 16 2. 4a 2 9 3. 25a 2 16b 2 4. 32x 2 y 18y 3 5. m 4 81n 4 10
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5.2.1: Factor the Square of a Binomial Squaring a binomial always results in three terms. Examples: (x + y) 2 = (x + y)(x + y) = x 2 + xy + xy + y 2 = x 2 + 2xy + y 2 (x y) 2 = (x y)(x y) = x 2 xy xy + y 2 = x 2 2xy + y 2 Examples: Factor the followings 1. x 2 6xy + 9y 2 2. x 3 y + 6x 2 y 2 + 9xy 3 11
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5.2.2: Factor the Sum and Difference of Cubes Two additional factoring patterns are the sum and difference of cubes. Examples: Factor the followings 1. x 3 + 27 2. 8w 3 27z 3 3. 5a 3 b 40b 4 Examples: y =9x 2 + 15x 1. Find y if x = 1. 2. Rewrite the polynomial equation by factoring the right side. 12
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5.3: Factoring Trinomials: Trial and Error Objectives: 5.3.1: Factor a trinomial of the form x 2 + bx + c 5.3.2: Factor a trinomial of the form ax 2 + bx + c 5.3.3: Completely factor a trinomial 13
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5.3.1: Factor a Trinomial of the Form x 2 + bx + c Recall that the product of two binomials may be a trinomial of the form ax 2 + bx + c This suggests that some trinomials may be factored as the product of two binomials. One process for factoring a trinomial into a product of two binomials is called trial and error . 14
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5.3.1: Factor a Trinomial of the Form x 2 + bx + c 15
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5.3.1: Factor a Trinomial of the Form x 2 + bx + c Examples: Factor the following trinomials. 1. x 2 + 7x + 10 2. x 2 9x + 14 3. x 2 + 4x 12 16
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5.3.2: Factor a Trinomial of the Form ax 2 + bx + c To factor a trinomial of the form ax 2 + bx + c, we must consider binomial factors of (_x + _) (_x + _) 17
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5.3.2: Factor a Trinomial of the Form ax 2 + bx + c Examples: Factor the following trinomials.
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  • Fall '18
  • jane
  • Accounting, Quadratic equation, Elementary algebra

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