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
    • 
      
      
    • 
      
  • ^{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
      • 64x^-1
      • x^3-216
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • x^3+27= (x^3)(x^2-3x+9)
      • 8x^3+27
      • x^3=25
• Binomial expansion
  • (a + b)³ = a^3+3a^2b+3ab^2+b^3
  • (a + b)⁴ = 

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.

End Behaviors/Naming Polynomials

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)