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:

Minipill

A type of birth control pill that contains only progestin, which is less likely to cause some of the side effects associated with estrogen-containing pills.

Oral Pills

A form of medication taken by mouth, specifically used here to likely refer to contraceptives used to prevent pregnancy.

Hormonal Methods

Contraceptive methods that use hormones to prevent pregnancy, such as the pill, patch, injection, and hormonal IUDs.

Oral Contraceptives

Medications taken orally to prevent pregnancy, commonly known as birth control pills.