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Find the multiplicity of the giver f(x)=(x-2)³ (x+3)⁴ *4x⁵

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Final answer:

The multiplicity of the given polynomial is 3, 4, and 5 for the factors (x-2), (x+3), and 4x respectively.

Step-by-step explanation:

The multiplicity of a given polynomial term is the number of times its corresponding factor appears in the polynomial. In this case, the given polynomial is f(x) = (x-2)³ (x+3)⁴ *4x⁵. To find the multiplicity of each term, we look at the powers of each factor.

The term (x-2)³ has a multiplicity of 3 because it is raised to the power of 3.

The term (x+3)⁴ has a multiplicity of 4 because it is raised to the power of 4.

The term 4x⁵ has a multiplicity of 5 because it is raised to the power of 5.

Therefore, the multiplicity of the given polynomial is 3, 4, and 5 for the factors (x-2), (x+3), and 4x respectively.

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