Identifying Special Situations In Factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• p² - 64 = p² - 8² = (p + 8)(p - 8)
• 121 - y² = 11² - y ² = (11 + y)(11- y)
• x² - 36y² = x² - (6y)² = (x + 6y)(x - 6y)
• Trinomial perfect squares
• a² + 2ab + b² = (a + b)(a + b) or (a + b)²
• x² + 6x + 9 = x² + 2(3)x + 3² = (x + 3)²
• x² - 10x +25 = x² - 2(5)x + 5² = (x - 5)² 
• x² - 5x + 25/4 = x²- 2(5/2)x + (5/2)²  = (x - 5/2)²
• a2 - 2ab + b2 = (a - b)(a - b) or (a - b) 
• 3² + 2(3)(5) + 5² =
• 7² + 2(7)(2) + 2² =
• 12² + 2(12)(9) + 9² =
• Difference of two cubes
• a³ - b³
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• 8x³ + 27 = (2x)³ + (3)³ = (2x + 3) (4x² + 6x + 9) 
•  10x³ + 30 = (4x)³ + (5)³ = (5x + 5) (6x² + 8x + 11)
•  6x³ + 25 = (x)³ + (2)³ = (2x + 4) (5x² + 4x + 10)
• Sum of two cubes
• a³ + b³ 
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
•  x³ + 64 = (x + 4)(x²
•  (x + a)(x² - ax + a²)
•  (4a)³ + (1)³ = (4a + 1)(16a² - 4a + 1- 4x + 16)
• Binomial expansion
• (a + b)³ = Use the pattern
• (a + b)⁴ = 

End Behavior

Domain - x values

Range - y values referred to as f(x)

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

 

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

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

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

NAMING POYNOMIALS: 

**Degree:
0- constant

1- linear

2- quadratic

3- cubic

4- quartic

5- quintic

TERMS:                           ****Number of terms is always one less than the degree.
monomial
binomial
trinomial
quadranomial
poynomial