1. Lesson 7.6
EQ: How do you factor a polynomial when leading coefficient is not 1?
Topic/Objective: To factor trinomials in the form ax2 +bx + c
Factor out 9
Factor
9(x – 5)(x + 1)

2. Factor the trinomial in the form ax2 +bx + c
EX: Factor
3x2 +16x + 5
( ) + ( )
Find two numbers with a sum of 16 and product of 15
(3x ) + ( )
15 and 1
(3x2 + 15x) + (1x + 5)
Factor each parentheses
3x(x + 5) + 1(x + 5)
Write answer in factored form
(3x + 1) (x + 5)

3. Example:
3x2 + 5x + 2
Factor
Replace the first and last terms
( ) + ( )
To find the middle terms, find two numbers that have a product of 6 and sum of 5.
(3x ) + ( )
Factor one or both the parentheses if needed
(3x2 + 2x) + (3x + 2)
x(3x + 2) +1(3x + 2)
2 and 3
Write in factored form
(x + 1) (3x + 2)

4. EX: Factor
2x2 + 21x – 11
Find two numbers with product of –22 and sum of 21
(2x )+( – 11)
(2x x)+(-1x – 11)
factor
22 and -1
2x(x + 11) –1(x + 11)
Write in factored form
(2x – 1) (x + 11)

5. 4x(2x + 5) + 1(2x + 5)
(4x + 1) (2x + 5)