Solve for q: Polynomial Factors Homework

In summary, to determine the value of q in the polynomial f(x) = x^3 + qx^2 - x - 2, divide the polynomial by x+1 and x-2 separately, and equate the remainders. This will give two expressions with q as the single variable. By evaluating f(-1) and f(2), you can solve for q. Don't be intimidated by the coefficient q, as it can be treated as any other variable in algebraic expressions.
  • #1
DanialD
8
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.
 
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  • #2
Is it because you don't know how to divide polynomials? Or are you intimidated by having q as a coefficient?
 
  • #3
well yeah, i don't know what to do with q.
 
  • #4
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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Related to Solve for q: Polynomial Factors Homework

What is a polynomial factor?

A polynomial factor is an expression that can be multiplied by another expression to get a specific result. In the context of solving for q in Polynomial Factors Homework, the polynomial factor refers to the expression that is being factored out in order to solve for q.

Why do we need to solve for q in polynomial factors?

Solving for q in polynomial factors allows us to find the roots or solutions to a polynomial equation. This is important in order to graph the equation, find the x-intercepts, and understand the behavior of the function.

What are the steps for solving for q in polynomial factors?

The steps for solving for q in polynomial factors are as follows:

  1. Identify the polynomial expression that is being factored.
  2. Determine the factors of the leading coefficient and constant term.
  3. Use the factors to create a list of possible rational roots.
  4. Use synthetic division or long division to test each root until one is found that results in a remainder of 0.
  5. Write the original polynomial expression as a product of the found root and the resulting quotient.
  6. Repeat the process with the quotient until all factors have been identified.
  7. Set each factor equal to 0 and solve for q to find the solutions to the original polynomial equation.

What are some common mistakes when solving for q in polynomial factors?

Some common mistakes when solving for q in polynomial factors include:

  • Forgetting to check all possible rational roots.
  • Using the wrong signs when testing the potential roots.
  • Making errors in the long division or synthetic division process.
  • Forgetting to set the factors equal to 0 and solve for q.
  • Using the wrong order or combination of factors when writing the original polynomial expression as a product.

How can I practice and improve my skills in solving for q in polynomial factors?

The best way to practice and improve your skills in solving for q in polynomial factors is to do lots of practice problems. You can find worksheets and online resources with various polynomial equations to solve. It is also helpful to check your answers and compare them to the correct solutions to identify any mistakes and understand how to correct them. Additionally, working with a tutor or joining a study group can provide additional support and opportunities for practice.

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