Maths q

So got 3n^2 +2
How do i write a statement for ii)like a proof one?

Well, clearly you got some a +2 at the end there. If you are going to divide that expression by 3, the first term will reduce down to an integer which is fine, but the +2 poses a problem whereby it would be the remainder of the division. Hence we do not obtain an integer overall.

We say one thing divides another if the remainder is 0, so can you see how the above works out?

So if you divide 3n^2 +2 by 3 you get n^2 + 2/3
why do you have to get an integer?

That's how divisibility is usually defined.

One integer divides another if the result is an integer.

Ah so do you just say it's not divisible by 3 because you don't get any integer value or something.
Here's what the ms says:

Essentially, but just saying that doesn't justify it. As I said previously, the +2 is the problem so you need to use it in your reason just as the mark scheme does.

Could you please tell me how I could word it That would be great

Why? The mark scheme is right there!

Ok quoting ms "3n2 is always a multiple of 3 so remainder after dividing by 3 is always 2"
How is remainder after dividing by 3 2?
if you divide 3n^2 +2 by 3 you get n^2 + 2/3
which means remainder = 2/3 so howd they get that?

That's not how remainders work...

A remainder is the 'extra' you need to get to your value;. i.e. when you divide 7 by 3, clearly you can take two steps of length 3 to reach 6 which is fine, then the extra step required is 1 to reach 7.

Yes that makes sense but i cant figure about what the remainder would be if you divide 3n^2 +2 by 3

Clearly, you take $n^2$ amount of steps of length 3 to reach some number, then you need to take 2 extra to reach $3n^2+2$

So two is the remainder

Oh ok but what is the meaning of n^2 + 2/3 when you divide 3n^2 +2 by 3 ?cause they mention that in the ms too

It shows that you're adding a fraction to an integer, so the result overall is not an integer.

Ok so when you do 7 divided by 3 you get 2 remainder 1 , when you do 3n^2 +2 divided by 3 you get n^2 + 2/3 and then where did the remainder go?
This is where my confusion stems from

7/3 = 2 remainder 1

(3n^2+2)/3 = n^2 remainder 2

Oh ok so taking the first one:
Instead of doing 7/3 we can do (6+1)/3 = (6/3) + (1/3) to give 2 remainder 1 which is the same thing as 2 + 1/3 --> is that how it works?

Yes.