Solve for q: Polynomial Factors Homework

AI Thread Summary
To solve for q in the polynomial f(x) = x^3 + qx^2 - x - 2, it is necessary to find the remainders of f(x) when divided by x + 1 and x - 2. Evaluating f(-1) and f(2) will yield expressions that include q. The key point is that these two remainders must be equal, leading to an equation that can be solved for q. Understanding polynomial division and evaluating the function at specific points is crucial for finding the solution. The discussion emphasizes that working with the variable q should not be intimidating.
DanialD
Messages
8
Reaction score
0

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.
 
Physics news on Phys.org
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
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Problem with a product of 2 remainders (polynomials)
Replies
4
Views
2K
Create a polynomial with desired characteristics, factoring
Replies
3
Views
2K
What is the remainder when polynomial f(x) is divided by x^3-x?
Replies
9
Views
3K
Remainder factor theorem: me reason this out
Replies
33
Views
4K
A tricky remainder theorem problem
Replies
15
Views
3K
Factor Theorem and Trigonometric Equations Help
Replies
1
Views
2K
Solve the given equation that involves fractional exponent
Replies
4
Views
2K
How to Solve for x: Factoring Polynomials Homework Statement
Replies
17
Views
2K
Solve the problem involving the cubic function
Replies
12
Views
2K
Show that ##f(x)=2',1',2'## in the irreducible Polynomial
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top