2. Do Now: Multiply 1) (x+8)(x+4) 2) (x-8)(x-3) 3) (x-8)(x+1) 4) (x+9)(x-5) Aim: How Do We Factor Trinomials?

3. A simple trinomial is of the form ax 2 + bx + c. The middle term of a simple trinomial is the sum of the last two terms of the binomials. The last term is the product of the last two terms of the binomials. The method used is the sum/product method. Look for two numbers that have a product equal to the last term and a sum equal to the numerical coefficient of the middle term. Factoring Simple Trinomials

4. Factor: 6a 2 + 42a + 72 = 6(a 2 + 7a + 12) = 6(a + 4)(a + 3) a 2 + 9ab + 20b 2 = (a + 4b)(a + 5b) Factoring Simple Trinomials

6. Factor: 3x 2 + 17x + 10 Factoring General Trinomials Divide 1 st term by the leading coefficient and multiply the last term by the leading coefficient Simplify ( x + 15)( x + 2) Factor x 2 + 17x + 30 and leave a space before each x (3x + 15)(3x + 2) Put 3 back into each binomial (x + 5)(3x + 2) Divide each binomial by the GCF if there is (are)

7. Factor: 3x 2 - 10x - 8 ( x – 12)( x + 2) (3x – 12)(3x + 2) (x – 4)(3x + 2) Divide 1st term by the leading coefficient and multiply the last term by the leading coefficient Simplify Factor x 2 + 17x + 30 and leave a space before each x Put 3 back into each binomial Divide each binomial by the GCF if there is (are)

8. 1. 6x 2 + x – 15 3. 3x 2 + 20x + 12 Factor the following trinomials 2. 12x 2 – 9x – 3 x 2 + x – 90 ( x + 10)( x – 9) (6x + 10)(6x – 9)(3x + 5)(2x – 3) 3(4x 2 – 3x – 1) 3( x +1)( x – 4) 3(4x + 1)(4x – 4) 3(4x + 1)(x – 1) 3(x 2 – 3x – 4) x 2 + 20x + 36(3x + 18)(3x + 2) (x + 6)(3x + 2)

9. Factor: 5(4 – 3x) + 8x(4 – 3x) =(4 – 3x)(5 + 8x) Factor: 2(5x + 2) 2 – 7(5x + 2) =(5x + 2)[2(5x + 2) – 7] =(5x + 2)(10x + 4 – 7) =(5x + 2)(10x – 3)

10. Factoring Expressions With Complex Bases (a + 2) 2 + 3(a + 2) + 2 Let A = (a + 2). A 2 + 3A + 2 = [(a + 2) + 2] [(a + 2) + 1] Replace (a + 2) with A. Factor the trinomial. Replace (a + 2) with A. Simplify. = (a + 4)(a + 3) = (A + 2)(A + 1)

11. Group into two binomials Factor by GFC if possible Factor by GFC Factor completely

12. Factor each trinomial if possible. 1) x 2 –10x + 24 2) x 2 + 3x – 18 3) 2x 2 – x – 21 4) 3x 2 + 11x + 10 5) 5(2x – 3) 2 + 9(2x – 3) 6) (x – 3) 2 – 6(x – 3) + 8 7) x 3 + 3x 2 – x – 3