Stuck on Polynomial Division Problem

Question

Trying to find the quotient and remainder of the problem below..but keep getting to wrong. Could someone demonstrate how to solve this correctly? enter image description here

Oh deal Hollie Mollie! In your $;8-th,,,9-th;$ lines why did you mess up with the descending powers of $,x,$ ?! It should be $,-4x^2+2x,$ and not $;2x-4x^2;$, as this can only contribute both to confuse you and anyone reading that...and indeed: the ninth line should be $,-4x^2+8x;$ ... — DonAntonio, Aug 08 '13 at 11:00
Condescending? You're asking about polynomial division and I'm stressing to you how important order and neatness is in these matters, and you think I'm condescending? — DonAntonio, Aug 08 '13 at 11:03
You must have all powers of $x$ present under the division symbol. Add a $0x^{2}$ in the appropriate spot. Incidentally, I would much rather go with synthetic division in this case. — Adrian Keister, Aug 08 '13 at 11:05
@AdrianKeister Thanks. Where is the appropriate spot to add 0x^2? — jaykirby, Aug 08 '13 at 11:21
@Babak, more commonly written as holy moley, or holy moly --- see http://dictionary.reference.com/browse/holy+moly — Gerry Myerson, Aug 08 '13 at 11:25
@jaykirby You need to have descending powers of $x$ in the dividend, so place it between the $-4x^{3}$ and the $2x$. — Adrian Keister, Aug 08 '13 at 11:28

score 3 · Answer 1 · answered Aug 08 '13 at 12:07

3

It seems that you would have saved yourself a little confusion if you had simply set up the polynomial long division as follows:

$$x - 2\; \overline{|\;\;x^5 - x^4 - 4x^3 + \color{maroon}{0x^2} + 2x + 3\;}$$

and proceeded from there. (I.e., by writing in and accounting for the "implicit term" $\color{maroon}{0\cdot x^2}$, you would have kept the division properly aligned, and saved yourself a bit of a headache.)

answered Aug 08 '13 at 12:07

amWhy

209,954

1

jaykirby: thanks for showing your work. You seem to know how to divide polynomials, but simply overlooked needing to keep track of "missing terms" as noted in my answer. Nice work, all-in-all. – amWhy Aug 08 '13 at 12:29
Did u see my comment above? I saw that Don said Hollie Mollie. It sounds to me that it is a funny word till the Gerry gave me that link. – Mikasa Aug 08 '13 at 21:32
@amWhy: Nicely shown! +1 – Amzoti Aug 09 '13 at 00:13
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@Sami Take some aspirin and call (the doctor) in the morning! (That's a cliche sort of comment in the US). The classic joke about trying to call an MD during off hours is the doctor's response "Take two aspirin and call me in the morning!" – amWhy Jun 24 '14 at 15:58

score 1 · Accepted Answer · answered Aug 08 '13 at 12:00

Let's see. In this division, i have used base $x$ and long division. Unlike ordinary long division, i have taken the negative of the subtractions, and added them. This is quicker when there are mixed signs involved.

The answer is read off as $x^4+x^3-2z^2-4x-6$ remainder $-9$

           (5)   (4)  (3)(2)  (1) (0)

                  1   1  -2   -4  -6    rem 9
          --------------------------       
    1, -2 )  1   -1  -4   0   2    3       
            -1    2
                  1  -4                        
                 -1   2
                 ======                    
                     -2    0
                      2   -4
                          -4    2
                           4   -8
                               -6  3
                                6 -12
                                   -9

      1    1  -2   -4   -6 
          -2  -2    4    8   12
                             -9   remainder
       1   1  -4    0    2    3

Stuck on Polynomial Division Problem

2 Answers2

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