Factoring + Discontinuities

​Factoring binomials and quadratics

​Binomials

-Factor GCF

​Quadratics

-Factor Common Factors
- "X-method"

​Factoring Binomials: GCF

Multiple Choice

   6m² + 16m

• 2(3m² + 8m)

• 2m(3m + 8)

• 2m(3m - 8m)

• not factorable

Multiple Choice

Factor:
p² - 14p

• p(1 - 14)

• 2p(p - 7)

• p²(1-14)

• p(p - 14)

Multiple Choice

$$3x+12x^2$$  

• $$3x(1+4x)$$  

• $$x(3x+12)$$  

• $$3(x+4x)$$  

• $$3x(4x)$$  

Multiple Choice

$$18x^2-9x$$  

• $$18x(x-2)$$  

• $$9x(9x-1)$$  

• $$9x(2x-1)$$  

• $$3x(6x-3)$$  

Multiple Choice

$$x^2-4x$$  

• $$(x+2)(x-2)$$  

• $$x^2(x-4)$$  

• $$4x(x-1)$$  

• $$x(x-4)$$  

​Quadratics: Case 1
Difference of Squares

​*Bonus Case*

Multiple Choice

Factor Completely:
x² - 36

• (x + 9)(x - 4)

• (x - 6)(x - 6)

• (x - 9)(x + 4)

• (x + 6)(x - 6)

Multiple Choice

factor completely 
81m² - 1 

• not factorable

• (m-9)(m+9)

• 9m(9m-1)

• (9m-1)(9m+1)

Multiple Choice

Factor:
x² - 49

• (x + 7)(x - 7)

• (x + 7)²

• (x - 7)²

• (x+7)(x-1)

Multiple Choice

4x² - 64y²

• Prime

• ( 2x - 32y) (2 x + 32y) 

• ( 2x - 8y) (2 x - 8y) 

• ( 2x - 8y) (2 x + 8y) 

​Factor Quadratics: X-Method

1. Factor GCF

2. Fill in Diagram

3. f₁ , f₂ : Factors of [ac] that add up to [b].

4. Reduce Ratios

5. Build Factors

​Factor the Quadratics using the X Method

Multiple Choice

What is the factored form of x²+16x+15

• (x+1)(x+15)

• (x+3)(x+5)

• (x-3)(x-5)

• (x-1)(x+15)

Multiple Choice

What is the factored form of x²-10x+24

• (x-4)(x-6)

• (x-12)(x+2)

• (x-8)(x-3)

• (x+24)(x-1)

Multiple Choice

What is the factored form of 25x²-9

• (5x+3)(5x-3)

• (x+5)(x-3)

• (x-3)(x+5)

• (5x+3)(3x+5)

Multiple Choice

Find the factors of 4x²-16x-9

• (2x-9)(2x+1)

• (2x+9)(2x-1)

• (4x-1)(x+9)

• (x+1)(4x-9)

Multiple Choice

What are the factors of 3x²-17x+10

• (x-5)(3x-2)

• (x+5)(3x+2)

• (3x-5)(x-2)

• (x+5)(3x-2)

Multiple Choice

What are the factors of x²-8x-48

• (x-12)(x+4)

• (x+12)(x-4)

• (x+12)(x+4)

• (x-12)(x-4)

​Identify the Discontinuities of the Function

​Homework 9/13-9/14

​1.3 # 1-4 Find each type of discontinuity for each function. Factor Numerator and Denominator if possible to find them.