Divide x^3-4x+1 by x-5: Is it Right?

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Homework Help Overview

The discussion revolves around dividing the polynomial x^3 - 4x + 1 by the linear term x - 5 using synthetic division. Participants are questioning the correctness of the initial results and the expected form of the outcome.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting synthetic division and expressing uncertainty about the results, particularly regarding the degree of the resulting polynomial and the remainder. Questions are raised about the correctness of the initial calculations and the implications of the division process.

Discussion Status

The discussion is ongoing, with some participants suggesting that the initial answers may not be correct. There is a call for showing work to clarify the process, and a reminder about the properties of polynomial division is introduced, indicating a potential direction for further exploration.

Contextual Notes

There is a mention of the expectation that dividing a cubic polynomial by a linear term should yield a quadratic result, which is being questioned. Additionally, the relevance of evaluating the polynomial at x = 5 to find the remainder is highlighted.

Sashman15
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Divide using synthetic division (x^3-4x+1) / (x-5)

i got x^3 + 1^2 -9 Remainder: 46.

is it right?
 
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Or is it 1x^3 - 9x^2 R: 46

?
 
i think your first answer is correct looking quickly becasue there is a place holder for the x^2 term resulting in 0
 
What am I missing?

You are using synthitic division to divide a cubic by a linear term. Should not your result be a quadratic? None of the suggestions made so far are correct.
 
As integral said it is not right. Why don't you show your work?
 
I might also point out that if you divide a polynomial, P(x), by the linear term x-a, the remainder is P(a). What do you get if you set x= 5 in
x3- 4x+ 1?
 

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