Module 3.3 Factoring

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)

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

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

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

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)

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