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.
confirm your posted expression for the divisor, D(x), please.

3. Originally Posted by skeeter
confirm your posted expression for the divisor, D(x), please.

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

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"

Thanks you for your patience.

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

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

$k+6 = -5$

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.