Troll question in the SAT math section

[Anonymous No.11876125]

So I took the practise SAT and I got a decent score and an almost perfect in the math section but the only question that didn't make no sense is pic related. It literally feels like a question specially meant to troll students.
The SAT otherwise was an average level of difficulty.

[Anonymous No.11876142]

>>11876125
look up “polynomial remainder theorem”

[Anonymous No.11876163]

(x-5)(x-2) satisfies it eliminating c
(x-1)(x-4) also satisfies it eliminating a,b
idk what d means but it's d by default?

[Anonymous No.11876184]

>>11876142
Ah, yes. That thing flew over my head and I kind of buried deeply in "my not important part of my brain". Is it important to remember that?

[Anonymous No.11876186]

>>11876163
literally just use p=-2 to realize a,b,c can't work

[Anonymous No.11876214]

p(x) = (x - 3)q(x) + r
You're given p(3) = -2
Must r = -2?

[Anonymous No.11876222]

>>11876214
You looked up? That's literally how the SAT officially explains it(with the same variables and all). Can you explain it?

[Anonymous No.11876254]

>>11876125
Just in general for the SAT, if you are stuck on a question, the best idea is to start figuring out which answers you know for sure are wrong.
A),B),C) can all be shown to be wrong via a counterexample. If you cant figure out conpletely, worst case you can increase your chances from 25% to at least 50% if you get rid of 2 wrong ones.

[Anonymous No.11876261]

>>11876254
>>11876142
it all makes sense a bit more, now that I have watched a few videos on "polynomial remainder theorem".

[Anonymous No.11876262]

>>11876125
Wait, American math exams have multiple choice questions?

[Anonymous No.11876266]

>>11876262
the standardized tests that hs students take can have multiple choice questions. you won't see this in most undergrad classes, and never past freshman year

[Anonymous No.11876267]

>>11876125
Polynomial = p(x)
p(3) = -2
What is true about p(x)?
>>11876163
D is basically a choice of words meant to confuse you with definitions. My guess is some boomer decide to obfuscate the question thus proving these standardized tests don't actually test for scholastic ability.

Any polynomial p(x) must have in its table 3 as an input equivalent to output -2. It is asking you what is true for p(x) not just p(3). It is also important to not get confused with binomials like >>11876163 did. Well that was the intention of the question but it's more easier to use binomials anyways to deduce what is true.

For answer D, the remainder for p(x) when it is divided by x-3 is equal to -2.

A good test taking strategy would be to skip this question if it is obfuscating with the definitions.
>>11876222
Look up the definition of a polynomial then break it down. A(x)^2 + b(x) + c

[Anonymous No.11876268]

>>11876262
The last 10 questions are not and this is the standard SAT which is necessary for everyone who is planning on going to college needs to take.

This is just one section of the exam. Overall the difficulty is about 7/10. Any person can get a decent score if they study for it.

[Anonymous No.11876295]

>>11876266
>>11876268
Interesting. Where I'm from they tried to introduce multiple choice questions on math exams and everyone was outraged.

[Anonymous No.11876305]

>>11876295
we have an abundance of stupid white trash human overflow, non-whites, and women in our educational system. If this were not the case we wouldn't have retarded things like multiple choice questions.

[Anonymous No.11876321]

>>11876295
Where exactly? I feel like the United States education system is the middle ground of education systems. It is standardise so that everyone has a fair chance and is mandatory if you want a decent career to at least finish the HS part, but is optional if you want to go the extra mile and is not as emphasise by the gov since almost anyone can have token jobs(onlyfans, YouTuber,etc)

[Anonymous No.11876337]

>>11876305
Well that's unfortunate. Multiple choice questions were shunned as a tool for politically motivated grade inflation.
>>11876321
Romania. According to mass-media and some politicians, the quality of our education has been steadily decreasing (i.e exams have been getting easier) but I'm not really sure what to think about that. If ours are bad then I guess that speaks volumes about other countries.

[Anonymous No.11876359]

>>11876337
It all depends on population, and sadly race diversity(science has proven that some races are simply not as smart as othera although they can if they work for it) and America has a
alot of that and increasing every year which is why out education is getting change every year to cater to the majority. Complaining about education is the equivalent of complaining about race diversity, overpopulation, and globalism.

[Anonymous No.11876395]

>>11876125
>not a
>not b
>not c
>therefore yes d
wow I solved your gay faggot problem without even bothering to read what d said

if you want to understand d, think of "completing the square" which gives a formula with a similar structure

[Anonymous No.11876407]

>>11876395
I got it. It's just

F(x) divided by X-K = Reminder

[Anonymous No.11876429]

>>11876125
By the division algorithm, we can write

p(x) = (x-3)q(x) + r(x)

where q(x) is some polynomial, and r(x) has degree < 1 (hence r(x) is constant). Since p(3) = -2, it follows that r(x) = -2. Hence the remainder when p is divided by x-3 is -2.

[Anonymous No.11876486]

>>11876337
>>11876359
Ethnically homogenous Romania ranks much lower in education than the United States you retarded /pol/yp.

[Anonymous No.11876502]

>>11876429
Why the r(x)?

[Anonymous No.11876524]

>>11876486
PISA scores are low for a variety of reasons including income disparity which results in fewer educational opportunities for a good chunk of students. The education system, if all goes well trains very competent pupils, and this is evidenced by international performances in various areas. For example, Romania has more prizes in the IMO than the USA and performs much better proportionally.

[Anonymous No.11876564]

>>11876502
This is the remainder term. If you divide a degree n polynomial by a degree m polynomial (assuming m < n) then the remainder is a polynomial of degree < m, since if it were >= m then you could take out one more of the degree m polynomial.

[Anonymous No.11876571]

>>11876564
I know but most people just write it as r not r(x).

[Anonymous No.11876594]

>>11876125
A
B
C

Would always have been wrong right? As there is no way to prove them, right?

[Anonymous No.11876595]

>>11876594
Forgot to add

Even if p(3) was equal to anything else.

[Anonymous No.11876602]

>>11876595
Even if p(3) was equal to zero which I think means that x-3 can be a factor of the polynomial. There would be no way to find out how which of the factors would correspond with it, right?

[Anonymous No.11876605]

>>11876602
Right?

[Anonymous No.11876608]

>>11876594
That's not how you disprove things. In this case you find a polynomial that fits and doesn't fit any of the three.
As anons pointed out already p(x) = -2 has the property p(3) = -2 and isn't divisible x-c polynomials, so assuming at least one answer is correct, D is the answer
>>11876602
if p(3) doesn't equal -2 then none of the answers are correct

[Anonymous No.11876671]

>>11876125
>p(x) = -(2/9)*x^2
>p(4) = - 3.5.....

[Anonymous No.11876778]

>>11876486
half of the children that participated in the tests in Romania were fucktards that skipped school even weeks before the tests.

not to mention, unlike the rest of the counties, Romania used a pen-and-paper test.
and in the end, I imagine a 15 yo Romanian student not giving a shit about a test that won't influence his HS admission grade.

[Anonymous No.11876897]

>>11876222
Its literally just fucking polynomial division.
Just divide the polynomial by x - 3.
Multiply the quotient by x - 3, then add the remainder, and you will get the polynomial.
You are multiplying the quotient by x - 3, so, if you plug in 3, then that term evaluates to 0.
The only term that counts at x = 3 is the remainder term.
If you are told that the polynomial is -2 at x = 3, then that means the polynomial division remainder (from dividing by x - 3) must be -2.

[Anonymous No.11876941]

Polynomial Remainder Theory

[Anonymous No.11876964]

Polynomial p(x) is in the form:
a_1x^n + a_2x^(n-1) + ... + a_(n-1)x^1 + a_n*x^0
We know that p(a) = y
To get a statement equivalent to r we can obviously plug in a for x in our equation, or we can factor out (x-a) because then when we plug in a for x it cancels out a bunch of terms. Whenever you divide a number (or polynomial) you have your
quotient and your remainder (a remainder being a fraction of the divisor) therefore:
p(x)/(x-a) = q(x) + r(x)/(x-a) ==>
p(x) = (x-a)q(x) + r(x) * 1 ==>
letting x = a ==>
p(a) = 0 * q(x) = r(a) ==> p(a) = r(a) ==>
r(a) = y if p(a) = y

[Anonymous No.11876971]

>>11876941
theorem*

[Anonymous No.11877013]

>>11876125
We can already guess that the most likely answer is D. From the description follows that p(3)+2=0
therefore, p(x)+2 is divisible by (x-3) without remainder.
therefore, if we divide p(x) by (x-3) the remainder would be -2

[Anonymous No.11877695]

>>11876524
It still contradicts your racist theory since aryan Romania is ranked lower than some more ethnically diverse countries with the same income level such as Uruguay, and it's also not far from the score of black Trinidad and Tobago. (>>11876486)

When compared to the USA that you seem to love to bash so much here, Romania is abysmal.

>>11876778
Cope

[Anonymous No.11877726]

>>11876186
if you're saying p(x) = -2 is a polynomial of order 0 so x doesn't have to be there that's pretty autistic but comfy

>>11876267
>thus proving these standardized tests don't actually test for scholastic ability.
you can train to take the test properly. iirc most math questions on the sat can be brute forced if you're fast, and you ought to since you only have so much time to actually do them

[Anonymous No.11877795]

>>11876125
No doubt this has been answered before, but clearly the answer is D. This is because:

1) On the meta level clearly answer D is quite different from the others and the others are clearly not true

2) p(x) + 2 has a zero at x=3. Therefore x-3 is a factor of p(x)+2. That is exactly what D is saying.

[Anonymous No.11878154]

>>11877695
Cope. The topic was high school mathematics, and we have much more impressive performances than the USA at the IMO, both in terms of overall prizes and other achievements
>Ciprian Manolescu (Romania) managed to write a perfect paper (42 points) for gold medal more times than anybody else in the history of the competition, doing it all three times he participated in the IMO (1995, 1996, 1997). Manolescu is also a three-time Putnam Fellow (1997, 1998, 2000)
Sure, the US might seem like the "better" country, but it's due to an interplay of numerous factors.

[Anonymous No.11878719]

>>11876125
Sorry if it is already answered, but I can't read an entire thread about high-school maths.
First of all, all questions are troll questions because they try to troll you into answering incorrectly. I assume that you understand that the first three choices are not necessarily true (you can come up with counter examples for each of them). Now, you know that for any polynomials p(x) and q(x) there exist polynomials such that p(x)=s(x)q(x)+r(x). If we take p(x) and (x-3) we get that there exist polynomials such that:
p(x)=(x-3)s(x)+r(x)
Now we evaluate the expression for x=3
p(3)=(3-3)s(3)+r(3), since p(3)=-2 and 3-3=0
-2=r(3)
Now let's talk about the reminder in polynomial division. The reminders rank is always less than the rank of q or else we could also pull another factor out of r which would be a multiple of q and add it to s (reducing the rank of r in the process). q here is (x-3). This means that the rank of q is 1 and according to the previous statement, it is necessary that the rank of r is 0. A polynomial with a rank of 0 is just a constant and its value we have determined already. Therefore r(x)=-2 for all x.

[Anonymous No.11878735]

>>11877726
>if you're saying p(x) = -2 is a polynomial of order 0 so x doesn't have to be there that's pretty autistic but comfy

there's nothing autistic about it, picking out limiting cases is one of the easiest ways to digest problems you don't immediately understand. in the case of this question it gives you the answer by process of elimination, even if you don't know why the answer is correct