How do I decide whether I need to take the positive or negative root of b^2?

if in doubt take the + version

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but why would the negative one not work and how would you know

So essentially, it would work. Think about it. You know that whenever your equations for A and B in terms of a and b hold, the factorisation is correct. Ergo so long as a and b are such that these equations hold, everything's fine.

but i got different values of A and B tho

I'm not sure what you mean..
I presume you have got to the point where you have, for the general case, two equations, I believe they were A = 2b - a^2 and B = b^2.
In this specific case, your A is -20, and your B is 16.
Therefore you simply need to find some a and b such that 16 = b^2 and -20 = 2b - a^2. So long as a and b satisfy these equations, you're fine. So for instance you could decide to pick b = -4, and then a^2 = 2b + 20 = 12, and you could pick a = root(12) (i.e. the positive root). The resulting factorisation will be correct. You could have picked b = 4 to begin with, or you could have picked a = -root(12) after picking b = -4, it all makes no difference.

I'm not sure what you mean..
I presume you have got to the point where you have, for the general case, two equations, I believe they were A = 2b - a^2 and B = b^2.
In this specific case, your A is -20, and your B is 16.
Therefore you simply need to find some a and b such that 16 = b^2 and -20 = 2b - a^2. So long as a and b satisfy these equations, you're fine. So for instance you could decide to pick b = -4, and then a^2 = 2b + 20 = 12, and you could pick a = root(12) (i.e. the positive root). The resulting factorisation will be correct. You could have picked b = 4 to begin with, or you could have picked a = -root(12) after picking b = -4, it all makes no difference.

okay i get you now, both of my solutions are correct, but when i was typing it in an online expand calculator i was typing it in wrong. the only problem I have is that the mark scheme only states the factorisation with the root28 as the correct answer and omits the answer with root12; would you get the marks if you just did the root 12 factorisation?