## Polynomial long division

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
Jherek2
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### Polynomial long division

Hi, I have this long division exercise and I am completely stumped. This is the last in a set of 26, the others I have done without a problem, but I can't see how to start this one. Where I am stuck is in trying to divide the lead term $17x^4$ by $-5x^2$, which doesn't go exactly, so I end up with a fraction and I don't know how to continue with that. I guess that there's a really simple thing I can't see that would make it easy, so a hint to get me started would be appreciated...
($17x^4+2x^3-39x^2-16x+10$)/($-5x^2-4x+2$)

stapel_eliz
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Jherek2 wrote:Hi, I have this long division exercise and I am completely stumped. This is the last in a set of 26, the others I have done without a problem, but I can't see how to start this one. Where I am stuck is in trying to divide the lead term $17x^4$ by $-5x^2$, which doesn't go exactly, so I end up with a fraction and I don't know how to continue with that. I guess that there's a really simple thing I can't see that would make it easy, so a hint to get me started would be appreciated...
($17x^4+2x^3-39x^2-16x+10$)/($-5x^2-4x+2$)

You're going to be stuck with fractions.

What do you get when you divide 17x^4 by -5x^2? You get -(17/5)x^2, so that's what goes on top.

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`a)               -(17/5)x^2               -----------------------------------------------5x^2 - 4x + 2 )  17  x^4 +    2  x^3 -    39  x^2 - 16x + 10                                 ----------------------------------------------                            `

Multiply this by all three terms of the divisor:

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`b)               -(17/5)x^2               -----------------------------------------------5x^2 - 4x + 2 )  17  x^4 +    2  x^3 -    39  x^2 - 16x + 10                  17  x^4 + (68/5)x^3 - (34/5) x^2               ----------------------------------------------                            `

Then subtract:

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`c)               -(17/5)x^2               -----------------------------------------------5x^2 - 4x + 2 )  17  x^4 +    2  x^3 -    39  x^2 - 16x + 10                  17  x^4 + (68/5)x^3 - (34/5) x^2               ----------------------------------------------                           -(58/5)x^3 - (161/5)x^2`

Then carry down the remaining terms:

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`d)               -(17/5)x^2               -----------------------------------------------5x^2 - 4x + 2 )  17  x^4 +    2  x^3 -    39  x^2 - 16x + 10                  17  x^4 + (68/5)x^3 - (34/5) x^2               ----------------------------------------------                            (78/5)x^3 - (161/5)x^2 - 16x + 10`

Then do the same thing for the next step.

Jherek2
Posts: 9
Joined: Sat Aug 04, 2012 2:45 pm
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### Re: Polynomial long division

Ah, thank you for that! I suspected it may be something like that, but it seemed so complicated, I was sure I was overlooking something simple.
I will give it a go and see if I can get it right!
Well the question in the book was find the remainder, which they gave as 2x^4, mine is below and try as I might I can't get 2x^4. I even put the question into Wolfram Alpha and got the same answer as mine, so I can't explain the 2x^4?

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`               -(17/5)x^2 + (58/25)x + (573/125)               -----------------------------------------------5x^2 - 4x + 2 )  17  x^4 +    2  x^3 -    39  x^2 - 16x + 10                  17  x^4 + (68/5)x^3 - (34/5) x^2               ----------------------------------------------                           - (58/5)x^3 - (161/5)x^2  - 16x + 10                           - (58/5)x^3 - (232/25)x^2 + (116/25)x^2                           -------------------------------------------------                                         -(573/25)x^2 - (516/25)x   + 10                                         -(573/25)x^2 - (2292/125)x + (1146/125)                                         ---------------------------------------                                                      - (288/125)x  + (104/125) remainder`