1. 9-4 Factoring Trinomials ax2 + bx + c
Objective #1: Factor trinomials of the form ax2 + bx + c
(2x + 3)(x + 2) =
**To factor quadratic trinomials of the form ax2 + bx + c, find two integers, m and n, whose sum is equal to b and whose product is equal to ac. Then use factoring by grouping to write in factored form.
Ex 1: Factor ax2 + bx + c
a) Factor 5x2 + 27x + 10
Identify a, b, and c
Factors of Sum Make an organized list of factors of 50
5x2 + 27x + 10 = 5x2 + mx + nx + 10
b) Factor 24x2 - 22x + 3
Factors of Sum Make an organized list of factors of 72
24x2 - 22x + 3 = 24x2 + mx + nx + 3

2. Factor out the GCF using the DP
Ex 2: Factor when a, b, and c have a common factor.
Factor 4x2 + 24x + 32
Find the GCF of 4, 24, 32
Factor out the GCF using the DP
STUDY TIP: Always check for a GCF before factoring a trinomial!!

3. Prime Polynomial--A polynomial that cannot be written as a product of two polynomials with integer coefficients.
Ex 3: Determine whether a polynomial is prime
Factor 3x2 + 7x - 5
GCF?
Identify a, b, and c
Factors of -15 Sum Make an organized list of factors of -15
STUDY TIP: Make sure you list all possible factors of mn, including positive and negative factors, before you decide if it's prime.

4. Objective #2: Solve equations of the form ax2 + bx + c = 0
Ex 4: Solve an equation by factoring
Solve 18x2 - 19x - 8 = 3x2 - 5x
Write in ax2 + bx + c = 0 form
Factor left side
Zero Product Property
Solve each equation