1. 6 – 4: Factoring and Solving Polynomial Equations (Day 1)
Objective: Factor polynomial expressions.
Use factoring to solve polynomial expressions.

2. Example 1: Factor the Trinomial
A ) 3x3 – 3x2 – 18x
GCF = 3x
3x (x2 – x – 6)
3x (x-3)(x+2)
B ) 80x4y + 44x3y2 - 16x2y3
GCF = 4x2y
4x2y(20x2 + 11xy – 4y2)
4x2y(5x + 4y)(4x - y)

3. Special Factoring Patterns: Sum of two cubes
2. Difference of two cubes

4. Factor each polynomial
Example 2:
Factor each polynomial
x3 + 27
(x + 3) (x2 – 3x + 9)
16u5 – 250u2
GCF: 2u2
2u2(8u3 – 125)
2u2(2u-5)(2u u – 25

5. For some polynomials you can factor by grouping pairs of terms that have a common monomial factor. The pattern for this is as follows.

6. Example 4: Factor the polynomial
7x3 – 7x2 + x - 1
(7x3 – 7x2) + (x – 1)
7x2(x – 1) + 1(x – 1)
(7x2 + 1)(x – 1)
3x6 – 3x4 + 2x3 – 2x
(3x6 – 3x4) + (2x3 – 2x)
3x4(x2 - 1) + 2x(x2 – 1)
(3x4 + 2x)(x2 – 1)
x(3x3 + 2)(x2 – 1)

7. HOMEWORK Tomorrow’s Work AM Objectives: #3 Factor Trinomials
#4: Factor Sum or Difference of 2 Cubes
Tomorrow’s Work
AM Objectives:
#83 Factor Polynomials into Binomials & Trinomials
#84 Factor by Grouping

8. Example 3: Factor the polynomial

9. An expression in the form
where u is any expression in x is said to be in quadratic form. The factoring techniques for quadratics (factoring, completing the square, and the quadratic formula) can be used to factor such expressions.

10. Example 3
Factor each polynomial