Polynomial Functions

degree
1. Odd
2. Even
leading coefficient
1. Positive
2. Negative
End behaviour
Domain
1. {x ∈ R}
Multiplicity
1. Multiplicity of 1
2. Multiplicity of 2
3. Multiplicity of 3
Factorization
1. Factor Theorem
  1. Long Division
    1. Remainder Theorem
  2. Synthetic Division
Intervals of Increase and Decrease
2. 1. Increasing
    1. x∈ (-∞,-2) ∪ (0,∞)
  2. Decreasing
    1. x∈ (-2,0)
3. 1. Increasing
    1. x∈ (-3,0) ∪ (2,∞)
  2. Decreasing
    1. x∈ (-∞,-3) ∪ (0,2)
Symmetry
1. Symmetry across the y-axis
  1. 1. Mirror image across the y-axis
2. Symmetry across the origin
  1. 1. Looks the same even after its flipped 180 degrees
Solving Inequalities
1. x³+7x²+10x ≥ 0
  1. x(x²+7x+10x) ≥ 0
    1. x(x+5) (x+2) ≥ 0
      1. f(x) ≥ 0 when
        x∈ [-5,2] ∪ [0,∞)

Resource summary

	Created by Mathew_George about 10 years ago