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Math III

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

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  1. Math III October 22nd, 2012

  2. Zeroes and their Multiplicity • Multiplicity refers to the number of times a factor appears in a polynomial.

  3. Example 1: (x - 3)(x + 2) • Zeroes: • each occur only once in the polynomial, so they have a multiplicity of __________

  4. 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 ________________

  5. Graphing multiplicity: • If the multiplicity is: • Even graph DOES NOT cross the x-axis • Odd graph DOES cross the x-axis

  6. 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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