1. Module 3.3
Factoring

2. Factoring Binomials
Find the Greatest Common Factor (GCF) for both terms.
Divide the original terms by the GCF.
The factored polynomial should be written in the form GCF(Term1+ Term 2)
Special Cases:
Difference of Squares: If both a and b are perfect squares then:
a² – b² = (a + b)(a –b)
If a and b are both perfect cubes then:
Sum of Two Cubes: a³ + b³ = (a+b)(a²-ab+b²)
Difference of Two Cubes: a³ - b³ = (a-b)(a²+ab+b²)

3. Examples
16m²n + 12mn²
x² - 16
x³ + 125

4. Factoring Polynomials with 4 Terms
Separate the four terms into two groups of two terms
Factor each binomial.

5. Factoring Trinomials Chart Method Factor out a GCF if possible.
Multiply first coefficient by third coefficient.
Find Factors of the product whose sum equal the 2nd coefficient
Substitute new factors in for 2nd coefficient creating 4 terms.
Group and factor binomials. Factored binomials must be equal
Combine outside factors with one of the binomials.
Examples:
7x²-16x+4
4x²+7x+3

6. Combining Functions Practice distributing polynomials
If f(x) = x g(x) = 3x²-x+4
1. Find f(x) + g(x)
2. Find f(x) – g(x)
3. Find f(x) · g(x)

7. Solving
Factor the polynomial and then set each factor equal to zero and solve.
Example: (x+2)(2x-5)
Solution: x = -2 and x = 5/2