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I'm trying to divide a cubic equation by a factor.

This is the equation: $$ -\lambda^3 -\lambda^2 + 10 \lambda - 8 = 0$$

and this is the factor : $(\lambda - 1)$

I Googled about it and I found the Euclidean division, but I couldn't find some understandable way to do it.

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marked as duplicate by user17762, Amzoti, Micah, Henry T. Horton, Jim Apr 30 '13 at 1:03

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2 Answers 2

Try googling "polynomial long division": You can go directly to this entry in Wikipedia:

Polynomial Long division

Dividing one polynomial by another proceeds just as long division proceeds. And the best way to see how it works is to see some examples (as the linked entry contains), and just try it, do it, practice it. It won't help you much to provide you with the result: you'll want to see "how" so you can use it here and in any other situation you'll be certain to run across.

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Does this help, Aimad? –  amWhy May 2 '13 at 1:44

$$\lambda^3+\lambda^2-10\lambda+8=(\lambda -1)(\lambda^2+2\lambda-8)=(\lambda-1)(\lambda-2)(\lambda+4)$$

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How does that show a "way to do it"? –  amWhy Apr 30 '13 at 0:13
    
As much as sending the OP to some link, which he could have googled by himself...:) Anyway, I try to make him think: (1) the division is exact since $\,1\,$ is a root of the cubic, (2) putting $\,\lambda -1\,$ and "completing powers" (for example, that $\,2\lambda\,$ must be there in the middle so that we'll get get $\,\lambda^2\,$ in the final outcome), etc. I'm assuming, of course, that the OP has already studied some long division... –  DonAntonio Apr 30 '13 at 0:17
    
The OP clearly stated that s/he tried Googling...but couldn't find anything. Read the question: "I Googled about it and I found the Euclidean division, but I couldn't find some understandable way to do it." –  amWhy Apr 30 '13 at 0:18
    
I have deleted several off-topic comments. Please try to stay constructive. –  Zev Chonoles Apr 30 '13 at 0:25
    
Thank you very much, @ZevChonoles . –  DonAntonio Apr 30 '13 at 1:58

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