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# Math III - PowerPoint PPT Presentation

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

October 22nd, 2012

• Multiplicity refers to the number of times a factor appears in a polynomial.

• Zeroes:

• each occur only once in the polynomial, so they have a multiplicity of __________

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 ________________

• If the multiplicity is:

• Even graph DOES NOT cross the x-axis

• Odd graph DOES cross the x-axis

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