can you show me how this problem is solved in detail by using long dividion? x^3 - 8 / x - 2?

Question

the problem is x^3 - 8 / x - 2 how is this solved by using long division

Answer 1

Heres another way using convolution

N = (n3,n2,n1,n0) = (1,0,0,-8)
D = (d1,d0) = (1,-2)

deconvolution
N/D = (a2,a1,a0)
if O(N) = O(D) + 2

convolution
N/D * D = (a2,a1,a0) * (d1,d0) = (n3,n2,n1,n0)

n3 = d1 * a2
n2 = d1 * a1 + d0 * a2
n1 = d1 * a0 + d0 * a1
n0 = d0 * a0

a2 = n3 / d1
a1 = (n2 - d0 * a2) / d1
a0 = n0 / a0

a2 = 1 / 1 = 1
a1 = (0 - (-2 * 1)) / 1 = 2
a0 = -8 / -2 = 4

N/D = (1,2,4) = x^2 + 2x + 4

Answer 2

Polynomial long division... Good times. Here goes the division with explinations for each line beside it.

_x^2__+2 x__+4 Okay, the broken line is just normal division
x-2)x^3 -8 thing. So the x^2 on top comes from
dividing x^3 by x, and now multiplying x^2 by
x^3-2x^2 x-2 gives you this line. Subtracting from x^3-8
2x^2 -8 gives you this line Now, we gotta put 2x on
2x^2-4x top and multiply to get this line, Subtracting
4x -8 again gives this line. Now we go back to
to the top and put the 4, multiply through
4x-8 to give us this line. Finally, we subrtact one
last time and we got no remainder.
So, we have x^3-8/x-2 = x^2+2x=4
Hope this helps! :-)
Damn this looks ugly in the end... It's so beautifully lined up in the text box here, but not on there... Darn! sorry.

Answer 3

Write it on your paper like you are dividing x-2 into x^3 -8 long division style. ( I can't do it on this window.)

Now, only consider the first term when you are dividing (that would be only the x).

Think what do I need to get from x to get x to the third? (You need to multiply by x squared)

Put that on the top bar and subtract down after multiplying thru like regular long division.


x^3 - 8
x^3 - 2x^2
-------------
2x^2 - 8 (here's where you subtracted down. Remember you are changing the signs on the bottom row cuz you're subtracting. now divide again considering only the x. How do you get from x to 2x^2?)

Multiply by +2x

Therfore,

-2x^2 -8

2x^2 -4x
--------------------
4x -8 (remember you are subtracting so that is why the sign changed, divide again)

you get + 4

multiply it out

4x -8

4x -8
-------------
0 (you changed the signs cuz you subtracted)

Answer is x^2 +2x + 4


Let's hope you understand this. I'm limited in this format. And I'm only showing you the subtraction part below the actual problem. Email me if you don't get it.

Answer 4

The dots are merely spacers - I don't know how to keep leading spaces in this Yahoo system - ignore the dots.

Write the problem like long division, suplying zero coefficients for the missing terms. Then divide the x into x^3 and proceed just like in long division.

...........x^2
........-------------------------
x - 2 ) x^3 + 0x^2 + 0 x - 8
..........x^3 - 2 x^2
..........-------------
..................2x^2 + 0x

Now divide the x into the 2x^2 and continue.

...........x^2 + 2x
........-------------------------
x - 2 ) x^3 + 0x^2 + 0 x - 8
..........x^3 - 2 x^2
..........-------------
..................2x^2 + 0x
..................2x^2 + 4x
..................------------
..........................- 4x - 8

Now the x into -4x.

...........x^2 + 2x - 4
........-------------------------
x - 2 ) x^3 + 0x^2 + 0 x - 8
..........x^3 - 2 x^2
..........-------------
..................2x^2 + 0x
..................2x^2 + 4x
..................------------
..........................- 4x - 8
...........................-4x +8
.........................----------
................................- 16

There would be no remainder if your original dividend was x^3 + 8, in which case your final answer would be

(x^3 + 8)/(x - 2) = x^2 + 2x - 4

Answer 5

You first have to write -pseudo-terms in the numerator:

x^3 + 0x^2 + 0x -8

You can't do long division without the "x^2" and "x" terms, but since the coefficients are zeros, its the same as x^3 - 8

___________ x^2 + 2x + 4
x - 2 | x^3 + 0x^2 + 0x -8
_____ -x^3 +2x^2

_______ 0 + 2x^2 + 0x
____________-2x^2 + 4x

______________0 +4x - 8
_________________-4x + 8

_____________________0

x^2 + 2x - 4 + 0/(x - 2)
=x^2 + 2x - 4

Answer 6

First you'll need to change the equation a bit.
x^3 + (0)x^2 + (0)x - 8 / x - 2

. . . . x^2 + 2x + 4
____________________
x - 2 | x^3 + 0x^2 + 0x - 8
. . . . .-x^3 + 2x^2
. . . . . . . . . . 2x^2 + 0x
. . . . . . . . . -2x^2 + 4x
. . . . . . . . . . . . . . . 4x - 8
. . . . . . . . . . . . . . . .-4x + 8
. . . . . . . . . . . . . . . . . . . . 0

Answer is x^2 + 2x + 4 with no remainder

Answer 7

(x^3 - 8)/(x - 2)

``````````````````x^2 + 2x + 4
(x - 2)/¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
``````/ x^3 + 0x^2 + 0x - 8
``````````````- 2x^2 + 2x^2
------------------------------------------
```````````````2x^2 + 0x
``````````````- 2x^2 + 0x
------------------------------------
`````````````````````````0x - 8
```````````````````````- 0x - 8
-----------------------------------
```````````````````````````````0

ANS : x^2 + 2x + 4

Answer 8

It can be done on a paper easily than here.

If you want it then contact me.

Answer 9

If you're smart enough to understand it, then you should be smart enough to answer it yourself.

Answer 10

(x^4-8-2x)/x