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Math 3 Warm Up Oct. 22, 2012

Math 3 Warm Up Oct. 22, 2012. 1. Tell whether (x – 3) is a factor of . Find all possible roots of . Then find the actual roots, if any. (Use notes from Thurs) Find the number of possible positive and negative roots of . October 22, 2012. Notes: Multiplicity.

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Math 3 Warm Up Oct. 22, 2012

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  1. Math 3 Warm Up Oct. 22, 2012 1. Tell whether (x – 3) is a factor of . • Find all possible roots of . Then find the actual roots, if any. • (Use notes from Thurs) Find the number of possible positive and negative roots of

  2. October 22, 2012 Notes: Multiplicity

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

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

  5. 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 ________________

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

  7. Example 3: The following graph shows an eighth-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+2+1+1+2+1

  8. Create the polynomial and sketch the graph of:negative leading coefficient, with real zeroes: 3 with a multiplicity of 2, -2 with a multiplicity of 3, and -5 with a multiplicity of 1

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