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Problem : What is the multiplicity of each root of P(x) = (x - 3)2(x - 5)3(x + 1)?

x = 3 has multiplicity 2.
x = 5 has multiplicity 3.
x = - 1 has multiplicity 1.

Problem : If x = 2 - 7i is a root of P(x), what is another root? Name one real factor of P(x).

Root: x = 2 + 7i.
Real factor: x2 - 4x + 53.

Problem : If x = 4 - 3i is a root of P(x) = x3 -12x2 + 57x - 100, factor P(x) completely.

P(x) = (x - 4 + 3i)(x - 4 - 3i)(x - 4)

Problem : If 2 + 5i is a root of P(x) = x3 -5x2 + 33x - 29, factor P(x) completely.

P(x) = (x - 2 + 5i)(x - 2 - 5i)(x - 1).

Problem : How many complex roots foes 4x5 +3x4 -2x3 + 1 have?

5.

Problem : How many complex roots does 3x4 +4ix3 +3ix2 +4x2 - 5ix - 2x + 5i - 7 have?

4.
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