Identifying Special Situations in Factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• a²- 9 = (a + 3)(a - 3)
• a²- 25 = (a + 5)(a - 5)
• a²- 4 = (a + 2)(a - 2)
• Trinomial perfect squares
• a² + 2ab + b²= (a + b)(a + b) or (a + b)²
• a² + 8a + 16= (a + 4)(a + 4) or (a +4)²
• a² + 12a + 36= (a + 6)(a + 6) or (a + 6)²
• a² + 10+25= (a + 5)(a + 5) or (a + 5)²
• ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
• a^{2 _} 6a + 9 = (a - 3)(a - 3) or (a - 3)²
• a^{2 _} 10a + 25 = (a - 5)(a - 5) or (a - 5)²
• a^{2 _} 8a + 16 = (a - 4)(a - 4) or (a - 4)²
• Difference of two cubes
• a³ - b³
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• a³ - 1 = (a - 1)(a² + a + 1
• a³ - 27 = (a - 3)(a² + 3a + 6)
• a³ - 64 = (a - 4)(a² + 4a + 16)
• Sum of two cubes
• a³ + b³ 
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• a³ + 1 = (a + 1)(a² - a + 1)
• a³ + 64 = (a + 4)(a² - 4a + 16)
• a³ + 125 = (a + 5)(a² - 5a + 25)
• Binomial Expansion
• (a + b)³ = a³ + 3a²b + 3ab² + b³= (a + 4) ³ = a³ + 12a² + 48a + 64
• (a + b)⁴ =a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴ = (a + 3) ⁴  = a⁴  + 12a³ + 54a² + 108a + 81

                        

Naming Polynomials
Degree	Terms
0--Constant	Monomial
1—Linear	Binomial
2—Quadratic	Trinomial
3—Cubic	Quadrinomial
4—Quartic	Polynomial
5—Quintic
6--nth

Examples:
5x - 2 = 0 is a linear binomial
with a degree of 1 and no turns. 
5x³ − 4x² + 7x − 8= 0 is a cubic quadrinomial 
with a degree of 3 and 2 turns.
x⁴ - x² + 4x - 24 = 0 is a quartic quadrinomial
with a degree of 4 and 3 turns.

Number of Turns is always 1 less than the degree

Linear Equations : Y=mx+b, 1 degree and 0 turns

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

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

Quadratic Equations: ax² + bx + c = 0, 2 degree and 1 turn  

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

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

 

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