Solve for q: Polynomial Factors Homework

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Homework Help Overview

The problem involves finding the value of the coefficient q in the polynomial function f(x) = x^3 + qx^2 - x - 2, based on the condition that the remainders from dividing by x + 1 and x - 2 are equal.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss evaluating the polynomial at specific points (-1 and 2) to find expressions involving q. There is uncertainty about how to handle the variable q in these evaluations.

Discussion Status

Some participants are exploring the evaluation of the polynomial at the specified points to derive expressions for the remainders. There is a recognition that both evaluations will yield expressions that can be compared, but clarity on the next steps is still needed.

Contextual Notes

Participants express concern about the presence of the variable q and its impact on their understanding of polynomial division and remainder evaluation.

DanialD
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Homework Statement


If we divide f(x)= x^3+qx^2-x-2 by x+1, we get the same remainder as if we divide it by x-2. Determine the value of q


Homework Equations



f(x)= x^3+qx^2-x-2

The Attempt at a Solution



I tried to plug in f(-1) into the equation, and then f(2) into the equation.. But i honestly do not understand how to go about finding the remainders.
 
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Is it because you don't know how to divide polynomials? Or are you intimidated by having q as a coefficient?
 
well yeah, i don't know what to do with q.
 
Don't be afraid of the q. If you evaluated f(-1), you should get an expression with q as the single variable. Likewise, you'll get another expression after evaluating f(2). Now, what do you know about f(-1) and f(2)?


69
 

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