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

3. 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

4. 3x2 + 11x + 10 (3x )(x ) Example 1 Factor this quadratic: Step three:
Template
(3x )(x )

5. 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

6. 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

7. 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.

8. 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

9. 5x2 + 27x – 18 (5x )(x ) Example 2 Factor this quadratic: Step three:
Template
(5x )(x )

10. 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

11. 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

12. Assignment
6.5 Worksheet