End Behaviors

domain approaches positive infinity, range approaches positive infinity (rises right)
domain approaches negative infinity, range approaches negative infinity (falls left)

domain approaches negative infinity, range approaches positive infinity (rises left)

domain approaches positive infinity, range approaches negative infinity (falls left)

domain approaches positive infinity, range approaches negative infinity (falls right)

domain approaches negative infinity, range approaches negative infinity (falls left)

Degree
0- constant
1-linear
2-quadratic
3-cubic
4-quantic
5-quintic

Terms

monomial

binomial

trinomial

quadrinomial

polynomial

Special situations in factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• x^2 - 5^2= (x+5)(x-5)
• 3^2 - 4^2= (3+4)(3-4)
• 6^2 - y^2=(6+y)(6-y)

Trinomial perfect squares 

• a² + 2ab + b² = (a + b)(a + b) or (a + b)²
• x^2+ 10x + 25=(x+ 5)(x + 5) or (x + 5)²
• 2^2+ 16x + 16=(2+ 4)(2 + 4) or (2 + 4)²
• y^2+ 12y + 36=(y+ 6)(y + 6) or (y + 6)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
      • 8x³ + 27 = (2x)³ + (3)³ = (2x + 3) (4x² - 6x + 9)
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
• Binomial expansion
• (a + b)³ = (a+b)(a+b)(a+b)
• (a + b)⁴ = (a+b)(a+b)(a+b)(a+b)