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Math III. October 22 nd , 2012. Zeroes and their Multiplicity. Multiplicity refers to the number of times a factor appears in a polynomial. Example 1: (x - 3)(x + 2). Zeroes : each occur only once in the polynomial, so they have a multiplicity of __________.

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math iii

Math III

October 22nd, 2012

zeroes and their multiplicity
Zeroes and their Multiplicity
  • Multiplicity refers to the number of times a factor appears in a polynomial.
example 1 x 3 x 2
Example 1: (x - 3)(x + 2)
  • Zeroes:
  • each occur only once in the polynomial, so they have a multiplicity of __________
example 2 x 3 4 x 2 7
Example 2: (x – 3)4(x + 2)7
  • Zeroes: __________________
  • (x – 3) occurs ________________
  • (x + 2) occurs ________________
  • So, the root x = _________ has a multiplicity of _______________

and x = __________ has a multiplicity of ________________

graphing multiplicity
Graphing multiplicity:
  • If the multiplicity is:
    • Even graph DOES NOT cross the x-axis
    • Odd graph DOES cross the x-axis
slide6
Example 3: The following graph shows a fifth-degree polynomial. List the polynomial’s zeroes with their multiplicities.

Zeroes:

Crosses the x-axis @

Touches the x-axis @

If you add their minimum multiplicities, 1+1+1+1+1

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