2. Factoring Trinomials 3Trinomial – 3 terms. second termthird termWhen factoring a trinomial, we need to look at the second term and the third term to help find the factors. The factors of a trinomial will be two binomials.The factors of a trinomial will be two binomials.

3. Let’s take a Look y 2 + 3y + 2 What two numbers add up to +3 ( 2 and 1 ) Same two numbers that multiply to give you +2 Factors: Middle Term: Sum of 3 Last Term: Product of 2 Options: 1 and 2 Therefore: y 2 + 3y + 2 = (y + 1)(y + 2)

4. Let’s take a Look g 2 – 4g + 3 What two numbers add up to -4 Same two numbers that multiply to give you 3 Factors: Middle Term: Sum of -4 Last Term: Product of 3 Options: 1 and 3 or -1 and -3 Therefore: g 2 – 4g + 3 = (g - 1)(g - 3)

5. Let’s take a Look x 2 – 7x + 12 What two numbers add up to -7 Same two numbers that multiply to give you 12 Factors: Middle Term: Sum of -7 Last Term: Product of 12 Options: 1 x 12 or -1 x -12 2 x 6 or -2 x -6 3 x 4 or -3 x -4 Which gives a sum of -7? (-3) + (-4) Therefore: x 2 – 7x + 12 = (x - 4)(x - 3)

6. Chart to Help with Signs Sum ( 2 nd Term) Product ( 3 rd Term) INTEGERS Negative Bigger #(-) Smaller # (+) NegativePositiveBoth Negative numbers PositiveNegativeBigger # (+) Smaller # (-) Positive Both Numbers Positive

7. x 2 + 6x + 8 What two numbers add up to + 6 Same two numbers that multiply to give you 8 Factors: Middle Term: Sum of 6 Last Term: Product of 8 Options: Which gives a sum of +6? Therefore: x 2 + 6x + 8 = (x )(x )

8. x 2 + 6x + 8 What two numbers add up to + 6 Same two numbers that multiply to give you 8 Factors: Middle Term: Sum of 6 Last Term: Product of 8 Options: 1 x 8 or -1 x -8 2 x 4 or -2 x -4 Which gives a sum of +6? (2 and 4) Therefore: x 2 + 6x + 8 = (x + 2)(x + 4)

9. x 2 + 2x - 15 What two numbers add up to + 2 Same two numbers that multiply to give you -15 Factors: Middle Term: Sum of 2 Last Term: Product of -15 Options: Which gives a sum of +2? Therefore: x 2 + 2x - 15 = (x )(x )

10. x 2 + 2x - 15 What two numbers add up to + 2 Same two numbers that multiply to give you -15 Factors: Middle Term: Sum of 2 Last Term: Product of -15 Options: 1 x 15 or -1 x -15 3 x 5 or -3 x -5 Which gives a sum of +2? -3 and +5 (use chart to help with signs) Therefore: x 2 + 2x - 15 = (x -3)(x + 5)

11. y 2 - 4y - 12 What two numbers add up to - 4 Same two numbers that multiply to give you - 12 Factors: Middle Term: Sum of - 4 Last Term: Product of -12 Options: Which gives a sum of - 4? Therefore: y 2 – 4y - 12 = (y )(y )

12. y 2 - 4y - 12 What two numbers add up to - 4 Same two numbers that multiply to give you - 12 Factors: Middle Term: Sum of - 4 Last Term: Product of -12 Options: 1 x 12 or -1 x -12 2 x 6 or -2 x -6 3 x 4 or -3 x -4 Which gives a sum of - 4? - 6 and + 2 Therefore: y 2 – 4y - 12 = (y - 6)(y + 2)

13. y 2 - 5y + 4 What two numbers add up to - 5 Same two numbers that multiply to give you + 4 Factors: Middle Term: Sum of - 5 Last Term: Product of + 4 Options: Which gives a sum of - 5? Therefore: y 2 – 5y + 4 = (y )(y )

14. y 2 - 5y + 4 What two numbers add up to - 5 Same two numbers that multiply to give you + 4 Factors: Middle Term: Sum of - 5 Last Term: Product of + 4 Options: 1 x 4 or -1 x -4 2 x 2 or - 2 x -2 Which gives a sum of - 5? -1 and - 4 Therefore: y 2 – 5y + 4 = (y -1)(y - 4)

15. Class work Check solutions to Lesson 28(2) on my deskCheck solutions to Lesson 28(2) on my desk Lesson 29 worksheetLesson 29 worksheet Reminder that Solutions are on my deskReminder that Solutions are on my desk