Factor the Polynomial $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$

question 56

Essay

Factor the polynomial $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$ completely and find all its zeros. State the multiplicity of each zero.

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Definitions:

Foundations

Organizations established with the purpose of providing financial support to charitable causes, often endowed by a single benefactor.

Glass-Ceiling Effect

a barrier to advancement that is not officially acknowledged, limiting the progression of minorities and women in professional environments.

Career Advancement

The progression through a career path, which might involve upward movement, increasing responsibility, and higher compensation.

Invisible Barrier

A term often used to describe unseen obstacles preventing certain groups from advancing within an organization or system, such as the "glass ceiling" for women and minorities.