# Thread: Find the value of k using long division

1. ## Find the value of k using long division

Hello guys, I'm really stuck with this question in my assignment. I just wondering if you can give me an idea how to solve K using long division. Here is the function.

F(x) = x^5 - 3x^4 + 7x^3 + Kx^2 + 9x - 5; d(x) = x^2 - 1 +1

What I did here is I divided F(x) by D(x). But I dont know what to do with the K.

2. Originally Posted by cjru
Hello guys, I'm really stuck with this question in my assignment. I just wondering if you can give me an idea how to solve K using long division. Here is the function.

F(x) = x^5 - 3x^4 + 7x^3 + Kx^2 + 9x - 5; d(x) = x^2 - 1 +1

What I did here is I divided F(x) by D(x). But I dont know what to do with the K.

3. Originally Posted by skeeter

Sorry my divisor should be d(x) x^2-x+1

4. ## Find the value of K using long division

My divisor should be d(x) = x^2 - x +1

5. I did the long division, and assuming the quotient has no remainder, i get k = -11.

Code:
               x^3 - 2x^2 + 4x + (k+6)
.............------------------------------------
x^2-x+1 | x^5 - 3x^4 + 7x^3 + kx^2 + 9x - 5
x^5 - x^4   + x^3
..............------------------------------------
-2x^4  + 6x^3 + kx^2 + 9x - 5
-2x^4  + 2x^3 - 2x^2
....................--------------------------------
4x^3 + (k+2)x^2 + 9x - 5
4x^3 -  4x^2    + 4x
...............................--------------------------
(k+6)x^2 + 5x - 5
....................................... (k+6)x^2 - (k+6)x +(k+6)
-------------------------
last line ...

k+6 = -5
k = -11

6. ## Solving for K using a long division

Thank you very much for helping me. I just wanna clarify something. How did you get (k+2)x^2 .

2x^4 + 6x^3 + kx^2 + 9x - 5
-2x^4 + 2x^3 - 2x^2
--------------------------------
4x^3 + (k+2)x^2 + 9x - 5
4x^3 - 4x^2 + 4x

7. $\displaystyle kx^2 - (-2x^2) = kx^2 + 2x^2 = (k+2)x^2$

8. ## Solving for K using a long division

On the last line

(k+6)x^2 + 5x-5
(k+6)x^2 - (k+6)x + (k+6)

how did you arrived this "k+6 = -5"

9. $\displaystyle 5x - [-(k+6)x] = 0$

$\displaystyle 5x + (k + 6)x = 0$

$\displaystyle k+6 = -5$

10. ## Thank you very much

wow! Now everything is clear to me. Thank you very much Mr skeeter.

Godbless and keep up the good work.