Finding q when f(x) has equal remainders for divisors x+1 and x-2

[DanialD]

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.

 

[Hurkyl]

Is it because you don't know how to divide polynomials? Or are you intimidated by having q as a coefficient?

 

[DanialD]

well yeah, i don't know what to do with q.

 

[eumyang]

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)?


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