Gather Information on the Polynomial Using the Rational Roots Theorem

question 35

Essay

Gather information on the polynomial using the rational roots theorem, testing for 1 and -1, Descartes's rule of signs, and the upper and lower bounds property. Respond explicitly to each.
p(x) = x⁴ - 3x³ + 9x - 27

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Definitions:

Empty-Chair Dialogue

A gestalt therapy technique in which clients engage in a conversation with an imaginary person or part of themselves sitting in an empty chair, to explore different aspects of their psychology.

Real Feelings

Genuine emotions that an individual experiences, often contrasted with suppressed or socially conditioned responses.

Gestalt Therapy

An approach in mental health counseling that underlines personal accountability and zeroes in on the present moment experiences of the person seeking help, the rapport between therapist and client, the influence of social and environmental factors on an individual's life, and the personal modifications made in response to their broader context.

Emotional Flooding Therapies

Therapeutic techniques designed to expose individuals to a large amount of emotional stimuli with the goal of processing and overcoming intense emotions or traumas.