Help with Factoring Polynomials with Synthetic Division Code

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Summary:

Having trouble factoring quartics and higher using rational roots and synthetic division.

Help with Factoring Polynomials with Synthetic Division Code

RedWire77 02 Mar 2019 01:11

I wrote a program that will use synthetic division to check all of the possible rational roots of a polynomial and display which are actual roots, as well as the quotient after dividing with that root. It works perfectly for all quadratics and cubics I've tested (with only rational roots), but I cannot get it to work on quartics or higher for some reason. Can someone help me out?

As a side note, I'm fairly new to coding; I've been teaching myself for years and only recently started looking up the more advanced stuff. If there are possible improvements in my code, I would appreciate hearing those.

:1→N
:2→O
:ClrAllLists
:ClrHome
:Input "DEGREE:",D
:For(I,0,D
:ClrHome
:Disp "X^
:Output(1,3,D-I
:Output(1,5,"TERM
:Input ":",A
:A→L₁(I+1
:End
:ClrHome
:Disp "QUOTIENTS  ROOTS
:L₁(1→A
:Ans→L₄(1
:abs(L₁(D+1→B
:For(I,1,B
:If B/I=iPart(B/I
:Then
:B/I→L₂(N
:N+1→N
:End
:End
:1→N
:For(I,1,A
:If A/I=iPart(A/I
:Then
:A/I→L₃(N
:N+1→N
:End
:End
:dim(L₂ →L
:dim(L₃→M
:For(I,1,L
:For(J,1,M
:L₂ (I)/L₃(J→S
:L₁(1→N
:For(K,2,D+1
:L₁(K)+SN→N
:Ans→L₄(K
:End
:If not(L₄(D+1
:Then
:Disp S▶Frac
:Output(O,1,L₄
:O+1→O
:End
:L₁(1→N
:For(K,2,D+1
:L₁(K)-SN→N
:Ans→L₄(K
:End
:If not(L₄(D+1
:Then
:Disp -S▶Frac
:Output(O,1,L₄
:End
:End
:End

Re: Help with Factoring Polynomials with Synthetic Division Code

OneLetterShor 02 Mar 2019 17:15

I made a code like this. You can refer to it here: http://tibasicdev.wikidot.com/forum/t-10314293/synthetic-division
hope that it helps you!

Re: Help with Factoring Polynomials with Synthetic Division Code

RedWire77 02 Mar 2019 22:29

I saw your code, and the math in mine looks the same as in yours, although formatted slightly differently and I have my program check all possible rational roots instead of asking the user for roots to check. But because the math is accurate in both (and mine works for quadratics and cubics), I don't understand what is happening that causes quartics and higher-degree polynomials to be incorrect. From what I've checked, it stores the lists of the factors of the leading coefficient and the constant term correctly (rational roots theorem), but then performs the synthetic division incorrectly even though the math is right and it performs it correctly for low-degree polynomials.

Re: Help with Factoring Polynomials with Synthetic Division Code

RedWire77 04 Mar 2019 21:52

Nevermind, looks like it was just user error; the polynomials I was checking were distributed incorrectly, so they didn't actually have rational roots. I've rechecked with higher-degree polynomials that I confirmed have rational roots and it works. If anyone is interested in helping me improve the code, the current issues with it are: (1) it only shows up to 7 roots because I show the quotients from the synthetic division next to the roots in a vertical list; (2) if the same number comes up during the rational roots theorem tests, it shows up as a root both times (i.e. if 6/2 is tested and works, 3 will show up as a root, then 3/1 will also be tested and 3 will show up as a root again); and (3) if the quotient is too long, it will cover up the root (I could fix this with a conditional statement hiding the list if it is too long, but I don't know if I prefer that or not). I'm also unaware of a way to check for multiplicity of roots other than performing synthetic division again on a quotient of the root, so if someone else knows of a way I can work that in the code.