SOLUTION: I did the following problem by synthetic division. Since this problem is rather llloooonnnngggg, I decided I need to have someone double check this. Could a tutor please look this

Question 396190: I did the following problem by synthetic division. Since this problem is rather llloooonnnngggg, I decided I need to have someone double check this. Could a tutor please look this over and tell me if I've done this correctly? I would greatly appreciate it! Thx! Here is the problem:
x^7+x^5-10x^3+12/ (x+2)
Since the divisor isn't in "x-c" form, I had to alter that. Also, lots of terms were missing in this problem, so I had to alter that, too. (That is what made this problem looonnnggg!) After I altered it, the problem looked like this:
x^7+0x^6+x^5+0x^4-10x^3+0x^2+0x+12 / (x-(-2))
My synthetic division went like this:
-2_| 1 0 1 0 -10 0 0 12
-2 4 -10 20 -20 40 -80
_____________________________________
1 -2 5 -10 10 -20 40 -68 as remainder
So my answer is:
x^6-2x^5+5x^4-10x^3+10x^2-20x+40-68/(x-(-2))

YIKES!! Ok, is this correct, or do I need to go back to the drawing board with this? Any help would be welcomed!!! Thank you!!
Found 2 solutions by jim_thompson5910, CharlesG2:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You are correct.

Good job.

Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
"I did the following problem by synthetic division. Since this problem is rather llloooonnnngggg, I decided I need to have someone double check this. Could a tutor please look this over and tell me if I've done this correctly? I would greatly appreciate it! Thx! Here is the problem:
x^7+x^5-10x^3+12/ (x+2)
Since the divisor isn't in "x-c" form, I had to alter that. Also, lots of terms were missing in this problem, so I had to alter that, too. (That is what made this problem looonnnggg!) After I altered it, the problem looked like this:
x^7+0x^6+x^5+0x^4-10x^3+0x^2+0x+12 / (x-(-2))
My synthetic division went like this:
-2_| 1 0 1 0 -10 0 0 12
-2 4 -10 20 -20 40 -80
_____________________________________
1 -2 5 -10 10 -20 40 -68 as remainder
So my answer is:
x^6-2x^5+5x^4-10x^3+10x^2-20x+40-68/(x-(-2))

YIKES!! Ok, is this correct, or do I need to go back to the drawing board with this? Any help would be welcomed!!! Thank you!!"

x^7+x^5-10x^3+12/ (x+2)
filled in the missing terms with 0 coefficients
.................x^6 - 2x^5 + 5x^4 - 10x^3 + 10x^2 - 20x + 40
x + 2 --> x^7 + 0x^6 + x^5 + 0x^4 - 10x^3 + 0x^2 + 0x + 12
..........x^7 + 2x^6
..............- 2x^6 + x^5
..............- 2x^6 - 4x^5
.......................5x^5 + 0x^4
.......................5x^5 + 10x^4
............................- 10x^4 - 10x^3
............................- 10x^4 - 20x^3
......................................10x^3 + 0x^2
......................................10x^3 + 20x^2
............................................- 20x^2 + 0x
............................................- 20x^2 - 40x
......................................................40x + 12
......................................................40x + 80
...........................................................- 68
x^6 - 2x^5 + 5x^4 - 10x^3 + 10x^2 - 20x + 40 - 68/(x + 2) is answer
check:
(x + 2)(x^6 - 2x^5 + 5x^4 - 10x^3 + 10x^2 - 20x + 40 - 68/(x + 2)) -->
x^6(x + 2) - 2x^5(x + 2) + 5x^4(x + 2) - 10x^3(x + 2) + 10x^2(x + 2)
- 20x(x + 2) + 40(x + 2) - (68/(x + 2))(x + 2) -->
x^7 + 2x^6 - 2x^6 - 4x^5 + 5x^5 + 10x^4 - 10x^4 - 20x^3 + 10x^3 + 20x^2
- 20x^2 - 40x + 40x + 80 - 68 -->
x^7 + x^5 - 10x^3 + 12, yes
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