Identifying special situations in factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• (x + 9)(x − 9)
• (6x − 1)(6x + 1)
• (x³ − 8)(x³ + 8)
• Trinomial perfect squares
  • a² + 2ab + b²= (a + b)(a + b) or (a + b)²
    • x²-4x+4
    • 16x² - 8xy + y² = (4x - y)²
    • x²+6x+9
  • ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
• Difference of two cubes
  • a³ - b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 
        
        
        
        
        Sum of two cubes
• • a³ + b³ 
  • • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 
• Binomial expansion
•  

End Behaviors/Naming Polynomials

Linear Equations: 

y= mx+b 

1 degree

0 turns 

Domain - x values
Range - y values referred to as f(x)

When m is Positive: 

domain → +∞, range → +∞ (rises on the right)

domain → -∞, range → -∞ (falls on the left)

When m is Negative 

domain → -∞, range → +∞ (rises on the left)

domain → +∞, range → -∞ (falls on the right)

Quadratic Equations (parabolic equation)

y=ax² 

2 degree 

1 turn

(a+b)(c+d)

            

When a is Positive 

When a is Negative 

Naming Polynomials: 

--Number of turns is always 1 less than the degree. 

Degree:

0- Constant 

1- Linear

2- Quadratic 

3- Cubic

4- Quartic

5- Quintic 

6 to ∞- nth Degree 

Terms:

Monomial 

Binomial 

Trinomial 

Quadrinomial 

Polynomial 

domain → +∞, range → -∞ (falls on the right)

domain → -∞, range → -∞ (falls on the left)

domain → +∞, range → +∞ (rises on the right)

domain → -∞, range → -∞ (falls on the left)