What is the depressed polynomial for f(x) with an obvious root?

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    Depression Polynomials
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SUMMARY

The discussion focuses on finding the depressed polynomial for the function f(x) = x5 - 0.5x4 - 5.5x3 - 3.5x2 - 6.5x - 3, specifically when an obvious root is identified. Participants emphasize the importance of defining "depressed polynomial" and suggest using the Rational Root Theorem to identify potential roots. The conclusion is that there are four rational roots to test for this polynomial.

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lucifer_x
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how would i write the depressed polynomial for the obvious root of

f(x) = x5 - .5x4 - 5.5x3 - 3.5x2 - 6.5x - 3
 
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I am afraid you are going to have to define the term "depressed polynomial". I confess I don't recognize it. (Which makes me depressed!). I will also confess that I don't, offhand, see an "obvious" root to that polynomial!
 
Use rational roots theorem, you only have 4 roots to try.
 

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