Finding Values for k in f(x) = 2x^3+7x-3

  • Thread starter chris_tams
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In summary, the conversation discusses finding the values of k in the equation f(x) = 2x^3 + 7x - 3 when f(x) is divided by (2x-k) and the remainder is -8. The process involves using long division to find the remainder, which is equal to a cubic function in k. By equating the coefficients of the polynomial on both sides, the values of k and other variables can be solved for.
  • #1
chris_tams
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If i have f(x) = 2x^3 + 7x -3

And when f(x) is divided by (2x-k) I have -8

How do i find values for k?
 
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  • #2
I might be misunderstanding your question, but are you saying that

[tex]\frac{2x^3+7x-3}{2x-k}=-8[/tex]

and you wish to solve for k as a function of x?
 
  • #3
How do you actually divide 2 polynomials ? Do the long division ...you'll find the remaider to be R = f(k), where f is a cubic in k. Equate this to -8 and you have the 3 values of k.
 
  • #4
Yes and no there's no need to solve as a function of x: he's saying that if we write

2x^3+7x-3 = (2x-k)(x^2+ax+b)-8

what is k?

It's a division algorithm for polynomials question; by comparing coeffs on each side you ought to be able to solve a set of simulatneous equations to find k (and a and b)
 
  • #5
I'm assuming you mean the remainder is -8. It's not clear, and evidently, TALewis has interpreted differently.

And Matt's way is much easier.
 
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  • #6
Ah, if you mean the remainder is -8, that makes much more sense.
 
  • #7
yes, what i mean is that when, 2x^3+7x-3/(2x-k) This equals some polynomial funtion with a remainder of -8. How do i work out what the polynomial is?
 
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  • #8
Look at matt's post again.

Expand the RHS and equate coefficients of the different powers of x, between the LHS and RHS. For instance, "Is there an x^2 term in the LHS ?...No !" So you equate the coefficient in the RHS to zero...and so on. Solving from these equations gives you k.
 
  • #9
Yes youth. Cheers !
 

1. What is the value of k in f(x) = 2x^3+7x-3?

The value of k in this equation represents the constant term or the y-intercept. In this case, k is equal to -3.

2. How do you solve for k in f(x) = 2x^3+7x-3?

To solve for k in this equation, you can set x to 0 and solve for f(0). This will give you the value of k, which is -3 in this case.

3. Can the value of k in f(x) = 2x^3+7x-3 be a fraction or decimal?

Yes, the value of k can be a fraction or decimal depending on the coefficients in the equation. In this equation, k is a whole number, but it can also be a fraction or decimal in other equations.

4. What does the value of k represent in f(x) = 2x^3+7x-3?

The value of k represents the constant term or the y-intercept in the equation. It is the value of y when x is equal to 0.

5. How does changing the value of k affect the graph of f(x) = 2x^3+7x-3?

Changing the value of k will shift the entire graph of the equation up or down. A larger value of k will shift the graph higher, while a smaller value of k will shift the graph lower. The shape of the graph, however, remains the same.

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