1. Do Now: Aim: How Do We Factor Trinomials? Multiply 1) (x+8)(x+4)

2. Factoring Simple Trinomials
A simple trinomial is of the form ax2 + 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.

3. Factoring Simple Trinomials
6a2 + 42a + 72
a2 + 9ab + 20b2
= 6(a2 + 7a + 12)
= 6(a + 4)(a + 3)
= (a + 4b)(a + 5b)

5. Factoring General Trinomials
Factor: 3x2 + 17x + 10
Divide 1st term by the leading coefficient and multiply the last term by the leading coefficient
Simplify
Factor x2 + 17x + 30 and leave a space before each x
( x + 15)( x + 2)
(3x + 15)(3x + 2)
Put 3 back into each binomial
Divide each binomial by the GCF if there is (are)
(x + 5)(3x + 2)

6. Factor: 3x2 - 10x - 8 ( x – 12)( x + 2) (3x – 12)(3x + 2)
Divide 1st term by the leading coefficient and multiply the last term by the leading coefficient
Simplify
Factor x2 + 17x + 30 and leave a space before each x
( x – 12)( x + 2)
(3x – 12)(3x + 2)
Put 3 back into each binomial
Divide each binomial by the GCF if there is (are)
(x – 4)(3x + 2)

7. (x + 6)(3x + 2) Factor the following trinomials 1. 6x2 + x – 15

8. Factor: 5(4 – 3x) + 8x(4 – 3x) =(4 – 3x)(5 + 8x)

9. Factoring Expressions With Complex Bases
(a + 2)2 + 3(a + 2) + 2
Let A = (a + 2).
A2 + 3A + 2
Replace (a + 2) with A.
= (A + 2)(A + 1)
Factor the trinomial.
= [(a + 2) + 2] [(a + 2) + 1]
Replace (a + 2) with A.
= (a + 4)(a + 3)
Simplify.

10. Factor by grouping Group into two binomials Factor by GFC if possible
Factor completely

11. You Try It Factor each trinomial if possible. 1) x2 –10x + 24
7) x3 + 3x2 – x – 3