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. Chart to Help with Signs Sum (2 nd Term) Product (3 rd Term) INTEGERS NegativeNegative Bigger #(-) Smaller # (+) NegativePositive Both Negative numbers PositiveNegative Bigger # (+) Smaller # (-) PositivePositive Both Numbers Positive

4. Let’s take a Look x 2 + 7x + 6 What two numbers add up to +7 Same two numbers that multiply to give you +6 Therefore: x 2 + 7x + 6 = (x + 1)(x + 6)

5. Let’s take a Look a 2 – 8a + 12

6. Let’s take a Look m 2 – 5m - 14

7. Let’s take a Look Simplify, then Factor: -5r -3r 2 + 15 + 4r 2 – 3 – 3r -3r 2 + 4r 2 – 5r – 3r + 15 – 3 r 2 – 8r + 12 What two numbers add up to - 8 Same two numbers that multiply to give you + 12 Therefore: r 2 – 8r + 12 = (r -2)(r - 6) Factors:Sum: 1 x 12 -1 x -12 2 x 6 -2 x -6 3 x 4 - 3 x - 4 1 + 12 = 13 -1 + (-12) = - 13 2 + 6 = 8 -2 + (-6) = - 8 3 + (4) = 7 - 3 + (+4) = + 7

8. Let’s take a Look Factor Completely: 7q 2 – 14q -21 7(q 2 – 2q – 3) What two numbers add up to - 2 Same two numbers that multiply to give you - 3 Therefore: 7(q 2 – 2q – 3) = 7(q + 1)(q - 3) Factors:Sum: 1 x 3 -1 x -3 1 + 3 = 4 -1 + (-3) = - 4 1 + (-3) = -2 -1 + (3) = 2 Because the first term is not a one, consider factoring out the GCF

9. Let’s take a Look Factor Completely: 3x 2 + 21x + 57 3(x 2 + 7x + 19) What two numbers add up to 7 Same two numbers that multiply to give you 19 Therefore: 3(x 2 + 7x + 19) = 3(x 2 + 7x + 19) Because 19 is a prime and 1 and 19 can not give a sum of 7, we can not factor any further.

10. y 2 + 6y + 9 a 2 – 5a + 4 m 2 – m - 12 FACTOR COMPLETELY

11. SIMPLIFY, FACTOR COMPLETELY -5x + 5x 2 + 15 - 4x 2 – 3 – 3x 6y 2 – 12y - 18

12. Class work Worksheet 3-10bWorksheet 3-10b