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3.6 Solving by Factoring and Factoring Quadratics with Leading Coefficients
Objective: Solve quadratics by factoring. Be able to factor quadratics that start with a number other than 1.

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Step by step directions!
Standard Form? GCF? Factor. Set each factor to zero and solve. Check!

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Example 1 Factor this quadratic: 3×2 + 11x + 10 Step one: 3 • 10 = 30 Step two: Find a factor pair of 30 whose sum is 11.

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30 1 30 2 15 3 10 5 6 3×2 + 11x + 10 Example 1 Factor this quadratic:
1 30 2 15 3 10 5 6 31 17 13 11

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3×2 + 11x + 10 (3x )(x ) Example 1 Factor this quadratic: Step three:
Template (3x )(x )

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3×2 + 11x + 10 (3x )(x ) + 5 + 2 Example 1 Factor this quadratic:
Step four: (3x )(x ) Choose values that create the 5 and 6 from step 2. + 5 + 2

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3×2 + 11x + 10 (3x )(x ) + 5 + 2 Example 1 3×2 + 6x + 5x +10
Factor this quadratic: 3×2 + 11x + 10 Step five FOIL to check your work: (3x )(x ) 3×2 + 6x + 5x +10 3×2 +11x +10 + 5 + 2

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Example 2 Factor this quadratic: 5×2 + 27x – 18 Step one: 5 • -18 = -90 Step two: Find a factor pair of -90 whose sum is 27.

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Example 2 -90 -1 90 1 -90 -2 45 2 -45 -3 30 3 -30 Factor this quadratic: 5×2 + 27x – 18 89 -89 42 -42 There are more pairs here, but I stopped when I found the one I needed. 27 -27

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5×2 + 27x – 18 (5x )(x ) Example 2 Factor this quadratic: Step three:
Template (5x )(x )

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5×2 + 27x – 18 (5x )(x ) – 3 + 6 Example 2 Factor this quadratic:
Step four: (5x )(x ) Choose values that create the -3 and 30 from step 2. – 3 + 6

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5×2 + 27x – 18 (5x )(x ) – 3 + 6 Example 2 5×2 + 30x – 3x – 18
Factor this quadratic: 5×2 + 27x – 18 Step five FOIL to check your work: (5x )(x ) 5×2 + 30x – 3x – 18 5×2 +27x – 18 – 3 + 6

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Example 3 Factor this quadratic: 6×2 – 7x – 20 Step one: 6 • -20 = -120 Step two: Find a factor pair of -120 whose sum is -7.

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8 and -15 6×2 – 7x – 20 (6x )(x ) (3x )(2x ) Example 3
Factor this quadratic: 6×2 – 7x – 20 8 and -15 One of these can’t work. Which one can we rule out? Step three: Template (6x )(x ) (3x )(2x )

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6×2 – 7x – 20 (3x )(2x ) + 4 – 5 Example 3 Factor this quadratic:
Step four: (3x )(2x ) Choose values that create the 8 and -15 from step 2. + 4 – 5

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6×2 – 7x – 20 (3x )(2x ) + 4 – 5 Example 3 6×2 – 15x + 8x – 20
Factor this quadratic: 6×2 – 7x – 20 Step five FOIL to check your work: (3x )(2x ) 6×2 – 15x + 8x – 20 6×2 – 7x – 20 + 4 – 5

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Example 4 Factor this quadratic: 4×2 – 12x + 9 Step one: 4 • 9 = 36 Step two: Find a factor pair of 36 whose sum is -12.

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-6 and -6 4×2 – 12x + 9 (4x )(x ) (2x )(2x ) Example 4
Factor this quadratic: 4×2 – 12x + 9 -6 and -6 One of these can’t work. Which one can we rule out? Step three: Template (4x )(x ) (2x )(2x )

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4×2 – 12x + 9 (2x )(2x ) – 3 – 3 Example 4 Factor this quadratic:
Step four: (2x )(2x ) Choose values that create the -6 and -6 from step 2. – 3 – 3

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4×2 – 12x + 9 (2x )(2x ) – 3 – 3 Example 4 4×2 – 6x – 6x + 9
Factor this quadratic: 4×2 – 12x + 9 Step five FOIL to check your work: (2x )(2x ) 4×2 – 6x – 6x + 9 4×2 – 12x + 9 – 3 – 3

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Assignment 3.6 Worksheet

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