Identifying special situations in factoring

• Difference of two squares
  • a²- b² = (a + b)(a - b)
  • (x + 3)(x − 3)
  • (5x − 1)(5x + 1)
  • (x³ − 3)(x³ + 3)
• Trinomial perfect squares
• a² + 2ab + b² = (a + b)(a + b) or (a + b)²
• x² + 2x + 1 = 0
• x² + 4x + 2 = 0
• ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
• • 3 examples
• Difference of two cubes
  • a³ - b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
• Binomial expansion
  • (a + b)³ = Use the pattern
  • (a + b)⁴ = Use the pattern

Endbehaviors / Naming Polynomials

Linear Equation - y=mx+b

1 Degree

0 Turns

When M is positive - 

Raises to the Right, Falls to the Left.

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

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

When M is negative -

Raises to the Left, Falls to the Right.

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

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

Quadratic Equations - y=ax²+bx+c

2 Degree

1 Turn

(a+b)(c+d)

When A is positive - 

Raises Right, Raises Left

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

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

When A is negative -

Falls Left, Falls Right

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

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

Naming Polynomials

-Numbers of terms is always 1 less than degree

:Degree:

0- Constant 

1- Linear

2- Quadratic 

3- Cubic

4- Quartic

5- Quintic 

6 to ∞- nth Degree 

:Terms:

Monomial 

Binomial 

Trinomial 

Quadrinomial 

Polynomial