1. 6.5 Factoring Quadratics with Prime Leading Coefficients Objective: Be able to factor quadratics that start with a prime number.

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

3. Example 1 Factor this quadratic: 3x 2 + 11x + 10 30 130 215 310 56 31 17 13 11

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

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

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

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

8. Example 2 Factor this quadratic: 5x 2 + 27x – 18 -90 -190 1-90 -245 2-45 -330 3-30 89 -89 42 -42 27 -27 There are more pairs here, but I stopped when I found the one I needed.

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

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

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

12. Assignment 6.5 Worksheet