If we solve the equations:
$$x^3+2x^2-9x+2 = 0\\\therefore x = 3, -3, -2\\\therefore x = \pm3, -2$$
$$x^3-4 x^2+9 x-10\\\therefore x = 1+2i, 1-2i, 2\\\therefore x = 1\pm 2i, 2$$
It seems to me that $x = 1 \pm 2i, 2$ would fit better, as we know that it's the complex conjugate, and looks more tidy in both cases.
However my teacher says that it is improper notation, and will sometimes doc a mark if it's a large mark question.
I have also seen it in the data sheet for a few trig equations, such as:
$$\sin(A\pm B)=\sin\!A \cos\!B \pm \cos\!A\sin\!B\\
\cos(A\pm B)=\cos\!A \cos\!B \mp \sin\!A\sin\!B$$
Where the second is expanded into:
$$\cos(A + B)=\cos\!A \cos\!B - \sin\!A\sin\!B\\
\cos(A- B)=\cos\!A \cos\!B + \sin\!A\sin\!B$$
But when I used the same logic, for an answer. Of which I can't remember, which had the answers like:
$$y = (1 \pm x)(2 \mp x) \\\therefore y = (1+x)(2-x), (1-x)(2+x)$$
I was told that the former was wrong, and the latter was the answer.
I'm confused if how I'm using it is allowed, as the only time we use it is when we are solving square-roots, in which it's is implied by the square-root sign.
I think your use of $\pm$ is just fine. It seems to be widely used. I was told by one professor that writing things like $$i=1,2,3,4$$ was also improper and that I should rather use $i\in\{1,2,3,4\}$, but I have noticed that a lot of books and professors at my university use the former; including your use of the $\pm$ symbol.
However, if your teacher disagrees and claims to subtract points, you should just follow his notation for now.