3 6 Solving by Factoring and Factoring Quadratics

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! 1) Standard Form? 2) GCF? 3) Factor. 4) Set each factor to zero and solve. 5) Check!

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assignment 3. 6 Worksheet