1.5

• Zeros of Polynomial Functions

  • given a polynomial function p(x), if p(a) = 0, then a is a zero or root of p(x)
  • if a is a real number, then if x = a is a zero of p, then (x-a) is a linear factor of p
• Multiplicity (Repeated Zeros)

  • If a linear factor (x-a) is repeated n times, the corresponding zero of the polynomial has a multiplicity n.
  • The multiplicity of a zero is the degree of its factor. We can include the multiplicity when we list the zeros.
  • Odd: The graph crosses the x-axis
  • Even: The graph is tangent (touches) to the x-axis
• Complex Roots

  • Some polynomials have roots that contain an imaginary number. This means you will not see them on the graph.
  • All imaginary roots come in paris. If a + bi is a root of f(x), then so is a - bi. These are called conjugate pairs.
• Even Functions

  • an even function is symmetric over the y axis
  • f(-x) = f(x)
  • opposite inputs, same output
• Odd Functions

  • an odd function is symmetric over the origin
  • g(-x) = -g(x)
  • opposite inputs, opposite outputs
• • f(x) > 0 means the graph of f(x) is above the x -axis.
  • f(x) < 0 means the graph of f(x) is below the x -axis.