1) The document discusses factoring trinomials of the form x^2 + bx + c by using the FOIL method in reverse. 2) It provides examples of factoring trinomials with positive and negative signs using FOIL, and introduces a sign flowchart to determine the signs of the binomial factors. 3) The key steps are to write the trinomial as a product of two binomials, look at the signs to determine the signs in the binomial factors, then guess and check the last two numbers to fully factor the trinomial.

1. 7.3 Factoring TrinomialsObjective: To factor trinomials of the form x2 + bx + cFrameworks: 10.P.5

3. FOIL With a Negative and a Positive(x - 3)(x + 5)First terms: x and x x2Outside terms: x and 5 +5xInside terms: 3 and x -3xLast terms: 3 and 5 15Answer: x2 + 2x - 15

4. FOIL With a Negative and a Positive(x + 3)(x - 5)First terms: x and x x2Outside terms: x and 5 -5xInside terms: 3 and x +3xLast terms: 3 and 5 15Answer: x2 - 2x - 15

5. FactoringThe product of 2 binomials is usually a trinomial: (x + 3)(x – 2) = x2 + x - 6To factor a trinomial means to express it as a product of two binomials.To factor x2 + x – 6 is to rewrite it as (x + 3)(x – 2)

6. Signs Flowchart

7. FactoringTo solve this, we use FOIL in reverse: x2 + x – 6 = (x )(x )Now look at the signs: x2 + x – 6 = (x + )(x - )Then guess & check to find the last 2 numbers, remembering that the two terms multiplied are -6 and added are + 1x2 + x – 6 = (x + )(x - )

8. FactoringSolve: x2 - 2x – 48 = (x )(x )Now look at the signs: x2 -2x – 48 = (x + )(x - )Guess & check: x2 -2x – 48 = (x + )(x - )

9. Factor x2 - 13x + 40

10. Factor x2 + 11x + 24

11. Factor x2 - 15x + 56

12. Factor x2 - x - 20

13. Factor x2 - 2x - 24

14. Do p. 254 1-12