Find Factors of Polynomial Division: x-2 in Q[x] & x+1 in Z5[x]

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Homework Help Overview

The discussion revolves around polynomial division, specifically determining the values of k for which certain polynomials have specific linear factors in the contexts of rational coefficients and modulo arithmetic.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the initial steps necessary for polynomial division and the conditions under which specific factors exist. There is a question about how to begin the problem and what effort has been made prior to seeking help.

Discussion Status

The conversation is ongoing, with some participants seeking clarification on the problem setup and others emphasizing the importance of demonstrating prior effort. Guidance on the method of polynomial division has been suggested, but no consensus or resolution has been reached.

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There is an indication that participants must adhere to site policies regarding showing work before receiving assistance, which may affect the flow of the discussion.

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1. Polynomial division

a) For what values of k is x-2 a factor x^4 – 5x^3 + 3x + k in Q[x]?

b) For what values of k is x+1 a factor of x^4 + 2x^3 – 3x^2 + kx + 1 in Z5[x]
 
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Dash, you need to show what effort you have put into the problem before we can help you. This is both common sense and site policy. Until you are willing to do so, please stop posting your homework questions.
 
my problem is that I don't know how to start the problem?
 
Are you saying you do not know how to divide? "Polynomial division" is basically the same as "long division" in arithmetic: choose a "trial quotient" based on the term with the highest power, multiply by the divisor and subtract from the dividend. Repeat.
 

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