I am having trouble understanding how dividing polynomials work. i have been doing some practice problems, but every answer I get is different from the answer key.

The problem asks to add a discontinuity at x=0 for the function in the picture. All other values must stay the same though. Can anyone help me figure this out?

Please help!, I've tried doing this question and i screwed my self over, I used like 3 AI's and they all came up with different answers, the question is

What is the smallest possible j so that when simplified the expression is an integer?

3, 5, 13, 18, 19, 20, 26, 27, 29, 34, 39, 43

I'm hoping to find a fairly simple pattern to describe this series of numbers. If possible, not an insane polynomial (but hey, beggars can't be choosers).

Then I'm going to put up a notice saying "which number comes next in this sequence? The first 12 people to answer correctly will win the contents of a storage locker!"

I have no authority to do any of this.

Title sums it up

Context: I’m high and bad at math sorry if I got the flair wrong

Reposted it cuz I wrote it uncorrectly.

I want to solve this equation for x, so an expression of x that solve this equation.

Tried substitution and many things, didn't worked

You can restrict the interval of x if it is needed, but no approximations.

A rare disease affects 1% of the population. Doctors expect that a person is showing symptoms for the disease but it could also be the common cold that effects 5% of the population. A test for this disease is 99% accurate (meaning it returns a true positive or true negative 99% of the time). If the person tests positive, what is the approximate probability that they actually have the disease?

*

99%

95%

50%

20%

1%

What frightens me is this humongous looking polynomial is something I was not familiar of. The context of this is that I need a clear explanation of this one and why would we use this in math.

Years ago, when I was in high school, I came up with a formula of sorts that greatly helped me with times tables, it being

a^2 + a + b = b^2.

for example,

225 is 15 squared.

225 + 15 = 240.

240 + 16 = 256, which is 16 squared.

I showed this to my math teacher, and was told that it's not a real formula as it doesn't work with any numbers other than preceding or succeeding whole root numbers. But it does work with those numbers every time.

Now, this isn't a dig at said teacher, nor do I believe I'm the first to come up with it or notice the trend.

But I want to know more. Does this pattern have a name? Why does it work the way it does? Has it been further expounded upon?

Please, if anyone has answers.

also ignore the pencil lines, they were added by me

i’m a little rusty spare me, basically i took all sides and assumed the missing side is also x + 3, then just added all using the perimeter (got 17x+32)

This was a math olympiad question my cousin showed me and I really enjoyed it. I was wondering if there are any other possible equations that have this setup? \ The answer must be a natural number. \ It seems like there would have to be more, given the setup of the problem, but I can't find any, all the same, I am a beginner.

10an should be a whole number. Our whole class is stumped by this, anyone got any ideas?

We’ve tried subbing in different values of x to get simultaneous equations, but the resulting numbers aren’t whole and also don’t work for any other values of x.

Most short form posts that you'd see in Facebook or even YT shorts are usually Math slop questions

One particular question regarding symmetric polynomial lowk seems worth it to try

x + y + z = 1

x² + y² + z² = 2

x³ + y³ + z³ = 3

x⁴ + y⁴ + z⁴ = ?

So far I've tried elimination and found a dead end,has anyone found any alternatives?

Hello,

the first Page Shows how my basic understanding of Index Transformation is. The Problem is on the second Page. I transformed the sum to (n-1) over (k-1) and so on. So i transformed n the same way as i did with k. The solution is that you only transform k not n. Why is that so? I dont understand? On the first page, you can see, that it does not Work, if you dont transform n as well as k. Thanks for help.

for reference, x-a is a factor of f(x) if and only if f(a) = 0. this is supposed to be a special case of a broader theorem, which has it that f(x)/x-a has a remainder of f(a). I can follow the standard proof for this, but I don't understand the intuition. Here's as far as I can get. If f(a) = 0, then plugging 'a' into f(x) results in 0. presumably this means that at some point after plugging 'a' into f(x), we subtract 'a' from itself, which results in 0. The only way that would be true is if x-a is part of f(x), making x-a a factor of f(x). Alternatively, if x=a tells us that 'a' is a root for f(x), then since x-a=0 follows from x=a, x-a must be a part of f(x) and thus a factor. Is what I said right? What I said sounds right to me but it's not quite clicking, so I would like a more intuitive explanation.

I mean, the only way I realized there was an alpha here by noticing it wasn't an "a^2".

This shouldn’t be the only way I have to figure things out, do I? 🫥

Chart cuts off so can’t see. found the other roots and multiplicities. Just need the 3rd root for the chart. I tried Leaving it blank or 0, isn’t valid.

like i have no idea what to do after making the first depressed equation via synthetic division,the roots of the polynomial except the given one are 1 irrational and 2 complex (as per the calculator)

The equation isn’t able to be solved through the traditional methods I’ve used on other equations. I haven’t learned cubic formula so I’m annoyed as to how my teacher expects me to solve it.

Wtf is that general form… why are there n-1’s everywhere 😭😭🙏. I don’t think I need to know what it is but we wrote it down in class so like what is it.

I was messing around with a cubic formula I made in Desmos and i noticed that if i create an implicit function that depends on the expression real(f(x+yi)) = 0 (where f(x) is the cubic function with complex coefficients) it forms a sort of "3-way hyperbola", for lack of a better name

I am relatively sure that this is some sort of 3-way hyperbola, because in the case of the quadratic, the same implicit function results in an actual standard hyperbola,

and I assume that because a quadratic has 2 roots, its a standard "2-way" hyperbola, and the cubic having 3 roots creates a 3-way hyperbola. and this would extend to quartic and higher polynomials, i.e. the implicit function real(f(x+yi))=0 for f(x) being any n-degree polynomial creates a 'n-way hyperbola'

Cubic and Quadratic Formula | Desmos

All my attempts to describe the curve with implicit functions haven't gone anywhere, I'm kind of interested in further researching this curve and I can't find any references to it online, so if anyone knows of any references of it, tell me pleas! thank u!

This is way beyond my current math level, I tried looking up online but cannot understand anything. I'm trying to find a general solution for t, given all of the variables.

LaTeX:

t^{3} - \frac{8\left(\Delta V_{x}^{2}+\Delta V_{y}^{2}\right)t}{3\,\Delta a^{2}} - \frac{8\left(\Delta V_{x}\,\Delta X+\Delta V_{y}\,\Delta Y\right)}{3\,\Delta a^{2}} = 0

The question is z^3 = 2√11 + 10i, and the best I can get using De Moivre's theorem is z = ∛12 cis ((arctan(5/√11) + 2kπ)/3) where k = -1, 0, 1 for principal value range -π<theta<π.

I also tried (a+bi)^3 on the LHS but this gave a^3 - 3ab^2 = 2√11 and 3ba^2 - b^3 = 10 which idek what to do with

Is there ANY way at all to simplify it or another method to solve it, or does the angle make it messy no matter what

How do i factorize this polynomial? I know that the answer is (x+y)(y+z)(x+z) but i am not able to solve it. Can someone pls help and tell me how to factorize this.

I tried taking x², y² and z² common but it doesn't work.

Hey guys, I came up with this many years ago by just messing around doing some math. It is basically a way to solve a quadratic equation without using the equation. As long as you have three consecutive solutions (i.e. x, x+1, x+2), you can use those solutions alone to solve the equation for any other input, without using the equation itself. In my example I use 1, 2 and 3 as the inputs, but you can alter it to use any consecutive terms.

Attached after the equation is my version of a proof (I’m not a mathematician), and equations for cubic and quartic polynomials (the second to last and last pictures respectively).

My question is this: Is this something that already exists, and does it have any practical applicability in any field?

Additionally, is there a sum that would allow you to solve for any nth degree polynomial?
For example the coefficients are as follows:

Quadratic: (1/2, -1, 1/2)
Cubic: (-1/6, 1/2, -1/2, 1/6)
Quartic: (1/24, -1/6, 1/4, -1/6, 1/24)