How to divide 2 polynomials
(x^4 + 2x^3 + 4x^2 + 6x + 3)/(x+3)

Question

How to divide 2 polynomials
(x^4 + 2x^3 + 4x^2 + 6x + 3)/(x+3)

anonymous · Answer

factorize the numerator

anonymous · Answer

Than we will have (x(x^3 + 2x^2 + 4x + 6) + 3) / (x+3)
Is it possible to eliminate denominator completly?

anonymous · Answer

do u know how to do synthetic division

anonymous · Answer

https://www.youtube.com/watch?v=xY7Vpxvm62A check this video for synthetic division .. .

loser66 · Answer

If you want to completely eliminate the denominator, you must test whether -3 is a root of the numerator or not. If it is NOT a root of the numerator, then there is no way to completely eliminate the denominator. If it is, then you can do it by synthetic or long division.
How to test? just replace x = -3 into the numerator to see whether it is =0 or not. if it is =0 , then it is a root. if it is not, then it is not a root.

michele_laino · Answer

do you know Theorem of Ruffini? @Tmr

anonymous · Answer

@Michele_Liano No, where can I find accessible explanation?

michele_laino · Answer

I can teach you the so called "long division" if you want! @Tmr

loser66 · Answer

hahaha... look, how many people are here

anonymous · Answer

@Michele_Liano polinomial long division is what I look to learn and practice

michele_laino · Answer

ok! let's begin then, do you agree?

anonymous · Answer

yes

michele_laino · Answer

first step, please divide x^4 by x what is the result?

anonymous · Answer

x^3

michele_laino · Answer

perfect! now look at this drawing:

michele_laino · Answer

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