Objective: Solve quadratics by factoring.

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Solving Quadratic Equations by Factoring. Remember: When solving a quadratic equation by factoring, you must first start with an equation set equal to.

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Presentation transcript:

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.

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

Example 1 Factor this quadratic: 3x2 + 11x + 10 Step one: 3 • 10 = 30 Step two: Find a factor pair of 30 whose sum is 11.

30 1 30 2 15 3 10 5 6 3x2 + 11x + 10 Example 1 Factor this quadratic: 1 30 2 15 3 10 5 6 31 17 13 11

3x2 + 11x + 10 (3x )(x ) Example 1 Factor this quadratic: Step three: Template (3x )(x )

3x2 + 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

3x2 + 11x + 10 (3x )(x ) + 5 + 2 Example 1 3x2 + 6x + 5x +10 Factor this quadratic: 3x2 + 11x + 10 Step five FOIL to check your work: (3x )(x ) 3x2 + 6x + 5x +10 3x2 +11x +10 + 5 + 2

Example 2 Factor this quadratic: 5x2 + 27x – 18 Step one: 5 • -18 = -90 Step two: Find a factor pair of -90 whose sum is 27.

Example 2 -90 -1 90 1 -90 -2 45 2 -45 -3 30 3 -30 Factor this quadratic: 5x2 + 27x – 18 89 -89 42 -42 There are more pairs here, but I stopped when I found the one I needed. 27 -27

5x2 + 27x – 18 (5x )(x ) Example 2 Factor this quadratic: Step three: Template (5x )(x )

5x2 + 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

5x2 + 27x – 18 (5x )(x ) – 3 + 6 Example 2 5x2 + 30x – 3x – 18 Factor this quadratic: 5x2 + 27x – 18 Step five FOIL to check your work: (5x )(x ) 5x2 + 30x – 3x – 18 5x2 +27x – 18 – 3 + 6

Example 3 Factor this quadratic: 6x2 – 7x – 20 Step one: 6 • -20 = -120 Step two: Find a factor pair of -120 whose sum is -7.

8 and -15 6x2 – 7x – 20 (6x )(x ) (3x )(2x ) Example 3 Factor this quadratic: 6x2 – 7x – 20 8 and -15 One of these can’t work. Which one can we rule out? Step three: Template (6x )(x ) (3x )(2x )

6x2 – 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

6x2 – 7x – 20 (3x )(2x ) + 4 – 5 Example 3 6x2 – 15x + 8x – 20 Factor this quadratic: 6x2 – 7x – 20 Step five FOIL to check your work: (3x )(2x ) 6x2 – 15x + 8x – 20 6x2 – 7x – 20 + 4 – 5

Example 4 Factor this quadratic: 4x2 – 12x + 9 Step one: 4 • 9 = 36 Step two: Find a factor pair of 36 whose sum is -12.

-6 and -6 4x2 – 12x + 9 (4x )(x ) (2x )(2x ) Example 4 Factor this quadratic: 4x2 – 12x + 9 -6 and -6 One of these can’t work. Which one can we rule out? Step three: Template (4x )(x ) (2x )(2x )

4x2 – 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

4x2 – 12x + 9 (2x )(2x ) – 3 – 3 Example 4 4x2 – 6x – 6x + 9 Factor this quadratic: 4x2 – 12x + 9 Step five FOIL to check your work: (2x )(2x ) 4x2 – 6x – 6x + 9 4x2 – 12x + 9 – 3 – 3

Assignment 3.6 Worksheet