GIA

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GIA

• Lesson 4-4
• Factoring Trinomials
• ax2 bx c , a gt 1

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What You'll LearnWhy It's Important

• To solve problems using guess and check and
• To factor quadratic trinomials using the box and
  diamond method
• You can use factoring to solve problems involving
  shipping and geometry

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Factoring Trinomials

• 1. x2 6x 5
• 2. x2 4x 3
• 3. x2 5x 4
• 4. x2 4x 4
• 5. x2 x 2

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Factoring Trinomials

• 1. x2 6x 5
• 2. x2 4x 3
• 3. x2 5x 4
• 4. x2 4x 4
• 5. x2 x 2

(x5)(x1) (x 3)(x 1) (x 4)(x 1) (x
2)(x 2) (x 2)(x 1)
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Example 1

• Factor 17x 10 3x2
• Hint Before factoring a trinomial it must be
  written in descending order
• You must always look for the greatest common
  factor first
• If the coefficient of the squared term is greater
  than one that is what tells you to use the box
  and diamond method

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Example 1 SolutionBox and Diamond Method

• Factor 17x 10 3x2 ? 3x2 17x 10, no
  greatest common factor
• Draw a box put the first and last term diagonal
  from each other
• Then multiply those two terms together this will
  give you the top number in your diamond

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Example 1 SolutionBox and Diamond Method

• 3x2 17x 10
• 3x210 30x2
• What can you multiply to get 30 that adds up to
  17?

30
The middle term is the bottom of the diamond
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Example 1 SolutionBox and Diamond Method

• 3x2 17x 10
• 3x210 30x2
• What can you multiply to get 30 that adds up to
  17?
• Put those same two terms in your box multiplied
  by a variable

30
2
15
17
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Example 1 SolutionBox and Diamond Method

• 3x2 17x 10
• Now factor out the greatest common factor from
  each row and column
• The signs from your diamond apply to the box

30
15x
2
15
2x
17
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Example 1 SolutionBox and Diamond Method

• 3x2 17x 10
• Now factor out the greatest common factor from
  each row and column
• The signs from your diamond apply to the box

x
5
30
15x
3x
2
15
2x
2
17
The answer is (3x 2)(x 5)
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Example 2

• Factor 12x2 x - 6

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Example 2

• Factor 12x2 x 6
• The answer is (4x 3)(3x 2)

3x
-2
-72
-8x
4x
-8
9
9x
1
3
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Example 3

• Factor 30x2 -23x 3
• The answer is

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Example 3

• Factor 30x2 -23x 3
• The answer is (6x - 1)(5x 3)

5x
-3
90
-18x
6x
-5
-18
-5x
-23
-1
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Factoring Binomials

• Difference of Two Squares
• a2 b2 (a b)(a b) or (a - b)(a b)

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Examples

• 1. x2 16
• 2. x2 4
• 3. x2 1
• 4. 4x2 9
• 5. 9x2 4
• 6. 4x2 1
• 7. 16x2 25

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Examples

• (x 4)(x 4)
• (x 2)(x -2)
• (x 1)(x 1)
• (2x 3)(2x 3)
• (3x 2)(3x - 2)
• (2x 1)(2x 1)
• prime

1. x2 16 2. x2 4 3. x2 1 4. 4x2 9 5. 9x2
4 6. 4x2 1 7. 16x2 25
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THE END