1. Module 5.4 Factoring

2. Bell Ringer – End Behavior

3. Graphs and End Behavior LinearQuadraticCubic

4. Graphs and End Behavior ExponentialLogarithmic 

5. State the type of function and its end behavior.

6. 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)

7. Examples  16m²n + 12mn²  ax²- bx + a²y - b²y  x² - 16  x³ + 125

8. Factoring Polynomials with 4 Terms  Separate the four terms into two groups of two terms  Factor each binomial. The two remaining terms have to be equal.  Combine the two GCF and the two factored terms.  Example: ax²- bx + axy - by

9. Factoring Trinomials  Chart Method  Multiply first coefficient by third coefficient.  Find Factors of the product whose sum equal the 2 nd coefficient  Substitute new factors in for 2 nd coefficient creating 4 terms.  Group and factor binomials.  Combine outside factors with one of the binomials.  Examples:  7x²-16x+4  4x²+7x+3

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