Identifying Different Situations In Factoring

Identifying special situations in factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• (x + 9)(x − 9)
• (6x − 1)(6x + 1)
• (x³ − 8)(x³ + 8)
• Trinomial perfect squares
  • a² + 2ab + b²= (a + b)(a + b) or (a + b)²
    • 16x² - 8xy + y² = (4x - y)²
      
      
    • 8xy + y² + 16x² = 16x² + 8xy + y² = (4x + y)²
    • a² - 2ab + b² = (a - b)(a - b) or (a - b)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
      • x³-27 = (x-3)(x²+3x+9)
      • 8y³-125 = (2y-5)(2y²+10y+25)
      • s³-1 = (s-1)(s²+s+1)
• Sum of two cubes
  • a³ + b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • q³+1 = (q+1)(q²+q+1)
      • a³+125 = (a+5)(a²-5a+25)
      • h³+64 = (h+4)(h²-4h+16)
• Binomial expansion
• (a + b)³ = (a+b)(a+b)(a+b)
• (a + b)⁴ = (a+b)(a+b)(a+b)(a+b)

End Behaviors/ Naming Polynomials

Linear Equations:

y= mx+b

1 degree

0 turns

Domain - x values
Range - y values referred to as f(x)

When m is Positive:

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

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

When m is Negative

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

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

Quadratic Equations (parabolic equation)

y=ax²

2 degree

1 turn

(a+b)(c+d)

When a is Positive

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

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

When a is Negative

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

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

Naming Polynomials:

--Number of turns is always 1 less than the degree.

Degree:

0- Constant

1- Linear

2- Quadratic

3- Cubic

4- Quartic

5- Quintic

6 to ∞- nth Degree

Terms:

Monomial - one term

Binomial - two terms

Trinomial - three terms

Quadrinomial - four terms

Polynomial - two or more terms