Since no information is given on x, the first approach would be to substitute different values of x and check.
I substituted x=-10,-1,0,1,10 and concluded that A is always bigger than B

However, to ensure that this is indeed the case, I needed to use some algebra.

If A is always bigger than B, A-B will always be greater than 0

i.e. x^2 +3 - (3x -2) > 0
on solving the equality condition, the roots come out to be imaginary, showing that this equation is either always positive or always negative.
Now you can simply substitute a value and check if its positive or negative, or alternatively find the vertices and come to a conclusion that the equation A-B>0 is always true

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