1. Objective The student will be able to: factor quadratic trinomials. Trial and Error Method SOL: A.2c Designed by Skip Tyler, Varina High School

2. Factoring Chart This chart will help you to determine which method of factoring to use. TypeNumber of Terms 1. GCF 2 or more 2. Grouping 4 3. Trinomials 3

3. Review: (y + 2)(y + 4) Multiply using FOIL or using the Box Method. Box Method: y + 4 y y 2 +4y + 2 +2y +8 Combine like terms. FOIL: y 2 + 4y + 2y + 8 y 2 + 6y + 8

4. 1) Factor. y 2 + 6y + 8 Put the first and last terms into the box as shown. What are the factors of y 2 ? y and y y2y2 + 8

5. 1) Factor. y 2 + 6y + 8 Place the factors outside the box as shown. y2y2 + 8 y y What are the factors of + 8? +1 and +8, -1 and -8 +2 and +4, -2 and -4

6. The second box works. Write the numbers on the outside of box for your solution. 1) Factor. y 2 + 6y + 8 Which box has a sum of + 6y? y2y2 + 8 y y y2y2 y y+ 1+ 2 y + 8 y + 4 + y + 8y+ 4y + 2y

7. Algebraic Method Remember: (y + 2)(y + 4) = y 2 + (2+4)x + (2*4) = y 2 + 6x + 8 You multiply to get the constant term and add to get the linear term.

8. 2) Try one x 2 + 15x + 36 What do I multiply to get 36? 1 x 362 x 183 x 124 x 96 x 6 -1 x -36-2 x -18-3 x -12-4 x -9-6 x -6 Which set of numbers adds to give me 15? Answer: (x + 3)(x + 12)

9. Example: Factor Find 2 numbers a and b that multiply together to get 15 and add up 8. The numbers are: Now factor using the signs of the 2 numbers before them.

10. Factor Find 2 numbers a and b that multiply together to get +8 and add up -6. The numbers are: Now factor using the signs of the 2 numbers before them.

11. Factor Find 2 numbers a and b that multiply together to get -24 and add up 2. The numbers are: Now factor using the signs of the 2 numbers before them.

12. Factor Find 2 numbers a and b that multiply together to get -14 and add up -5. The numbers are: Now factor using the signs of the 2 numbers before them.

13. Summary for the signs for factoring a trinomial: If the sign of last is + then the 2 numbers have the same sign, which is the same as the middle sign. If the sign of last is - then the 2 numbers have opposite signs with the sign of middle going with the larger (greatest absolute value)

14. Examples: