Factor the Polynomial $p ( x ) = x ^ { 8 } + 16 x ^ { 5 } + 64 x ^ { 2 }$

question 70

Essay

Factor the polynomial $p ( x ) = x ^ { 8 } + 16 x ^ { 5 } + 64 x ^ { 2 }$ completely and find all its zeros. State the multiplicity of each zero.

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Definitions:

Isoprene

A simple hydrocarbon compound that serves as the monomer for natural rubber and is used in the synthesis of various polymers.

Cytotoxic Activity

The ability of a substance to kill or inhibit the growth of cells, often used in the context of cancer therapy.

Natural Product

Chemical compounds produced by living organisms, often used in pharmaceuticals, as agrochemicals, and in food additives.

Prostaglandins

Lipid compounds having diverse hormone-like effects in animals.