Keyed Math problem number 1

[ZOGs #1 Supporter]

Find a polynomial $f(x)$ of degree $5$ such that both the properties hold:
- $f(x)$ is divisible by $x^{3}$.
- $f(x)+3$ is divisible by $(x+1)^{3}$.

Write your answer in expanded form.

 

[ZOGs #1 Supporter]

A soysphere where math is the second soyjaks...
only if satan's laziness mouth shut...

esl + math is aryan, so aryan both nazi scientists and jews think it is good.

 

[ZOGs #1 Supporter]

@THE JOBBER OF THE SCHLOG
chatgpt or legit?

It's legit, but my in-depth explanation made a silly mistake (i mistook y(x) for f(x)). so ig now i must kms for being esl in math

 

[ZOGs #1 Supporter]

I'll use an online LaTeX interpreter/parser o algo (use a non-dark theme to actually see the mostly transparent images I sent ITP).

We start with these 2 equations:
View attachment 87137
The first equation is our 'divisible by $x^{3}$' statement and the second equation is our 'divisible by (x+1)^{3} after adding 3' statement.

Let's rewrite $y(x)$ and $g(x)$ into something more comprehensible (WOAHJAKS) and bring it to its logical conclusion.

View attachment 87144

The degree of $f(x)$ is $5$ and is divisible by $x^{3}$, therefore $f(x)$ must NOT have a constant, linear or quadratic term, thus making the equation look something like the above.

Unfortunately, it gets quite messy after this, bear with me thoughbeit.

We substitute $f(x)$ for its first equation into the second. We expand both equations and try to get the coefficients to equate to one another.

View attachment 87348
Therefore, $f(x)=18x^{2}+45x+30$

Okay, I gotta bounce, see you in an hour or 2.

@KingofTheRing check again nigga

 

[KingCargo]

@KingofTheRing check again nigga

You should check it again retard, I done the math and it’s 8.

 

[Starbing_Artiste]

MODS BAN XIM FOR SOLUTION FARMING

 

[ZOGs #1 Supporter]

MODS BAN XIM FOR SOLUTION FARMING

evandoe its for valid solutions, thus making it ok