Friday, November 19, 2010

Identifying special situations in factoring

  • Difference of two squares
    • a2- b= (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
    • a+ 2ab + b= (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
    • a- 2ab + b= (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
  • 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
        • 3 examples
  • Binomial expansion
    • (a + b)3 = (a+b)(a+b)(a+b)
    • (a + b)4 = (a+b)(a+b)(a+b)(a+b)

Thursday, November 18, 2010

End Behaviors

Domain - x values
Range - y values

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

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

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


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

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

    Terms
    monomial
    binomial
    trinomial
    quadrinomial
    polynomial