Multiply together

Factoring Polynomials Section 5-4 Pages 353-361

Objectives I can factor a polynomial using the following methods: GCF Reverse FOIL Difference of Two Squares Swing & Divide Grouping Sum of Two Cubes Difference of Two Cubes

Review: What is Factoring? Factoring is a method to find the basic numbers that made up a newly formed product.

Review In Chapter 4 we already covered these methods: GCF Difference of Two Squares Reverse FOIL Swing & Divide Now we will be looking at the other three methods

Sum of Two Cubes a3 + b3 = (a + b)(a2 – ab + b2) a3 + b3 = Here is the factoring rule: a3 + b3 = (a + b)(a2 – ab + b2)

Example 1 8x3 + 27 (2x)3 + (3)3 So a = 2x and b = 3 Factors are (a + b)(a2 – ab + b2) So: (2x + 3)(4x2 – 6x + 9)

Example 2 x3 + 64 (x)3 + (4)3 So a = x and b = 4 Factors are (a + b)(a2 – ab + b2) So: (x + 4)(x2 – 4x + 16)

Difference of Two Cubes a3 - b3 = Here is the factoring rule: a3 - b3 = (a - b)(a2 + ab + b2)

Example 1 64x3 - 1 (4x)3 - (1)3 So a = 4x and b = 1 Factors are (a - b)(a2 + ab + b2) So: (4x - 1)(16x2 + 4x + 1)

Example 2 8x3 - 125 (2x)3 - (5)3 So a = 2x and b = 5 Factors are (a - b)(a2 + ab + b2) So: (2x - 5)(4x2 + 10x + 25)

Grouping Method 4 Terms The grouping method uses a combination of GCF factoring with distributive property ra + rb + sa + sb (ra + rb) + (sa + sb) r(a + b) + s(a + b) (r + s)(a + b)

Example 1 x3 – 3x2 – 16x + 48 (x3 – 3x2) +(-16x + 48)

Example 2 x3 – x2 + 2x - 2 (x3 – x2) +(2x - 2) x2(x – 1) + 2(x – 1)

Homework Worksheet 10-4 TAKs Packet Objective #5 due next Monday