ANY HELP APPRECIATED, MULTIPLE QUESTIONS

This will be a lot, if you can answer any of my questions please do. The spreadsheet I'm referring to is in the files section below. (this will be multiple parts, as there seem to be too many characters)

Question 1- I have no idea where to even start with this, but I have different types of math formulas on the same spreadsheet (synthetic division, factor finding, and quadratic formula). Still, I need the answers for one math formula (factor finding) to find the numbers I need for the other two formulas (synthetic division and quadratic formula) which are not related at all, meaning I need different factors for each formula, but only have one factor finding section t the moment. I am trying to have the spreadsheet perform the necessary formulas as automatically as possible, so I have the numbers needed to find the necessary factors for the quadratic formula, but not for the synthetic division. Best case scenario, I want to be able to have both formulas automatically input the numbers into the factor finding section, but obviously this creates conflicting formulas and many errors. I'm thinking something akin to a button/on-off switch that determines which function's numbers are being inserted into the function-finding section, but I have no idea if that is even possible. If not, refer to question 2.

Question 2- If question 1 isn't possible, I want to repeat the formula in cell O3,  =LET(Num, N2, All, SEQUENCE(Num), Factors, FILTER(All, MOD(Num, All)=0), Factors), that I found at https://techcommunity.microsoft.com/t5/excel/need-help-with-a-function-formula-in-excel-to-determine-the/m-p/3865190/thread-id/196954, in cell I2, but have the resulting numbers display differently. Specifically, instead of displaying them below each other, as seen in column O, have them displayed left to right, top to bottom in cells I2:K8.

Question 3- Is there a way to automatically insert numbers from a list (I2:K8) into a cell (A1) until a different cell equals a certain number (G3=0)? This would be great on its own, but if I could also have Excel perform complete synthetic division (eg. automatically inserting numbers from a list (as said above) then inserting certain numbers (the numbers in B3:G3) into a different area (B1:G1) and repeating the formula until there are no numbers left? Along with automatically inserting the last number in B1:G1 into J1 to perform the formula mentioned in question 2?)

Any help at all would be amazing, but I know it's a lot to read and answer. This isn't super urgent, I just like making Excel calculators and this would help a ton for school. Any other mistakes you notice or ways I could make anything in the sheet more efficient, don't hesitate to let me know!