To solve this problem, let's find the electronegativity difference that we have between each pair of elements. If we look for the electronegativity of B, H and O we might find these values:
B: 1.5 O: 3.4 H: 2.1
So the two bonds that are present in our molecules have a difference of:
O ---- B = 3.4 - 1.5 = 1.9
H ----- B = 2.1 - 1.5 = 0.6
We have two types of covalent bonds, polar and non-polar. When the electronegativity difference is between 1.5 and 0.4 the bond is covalent polar, when it is less that 0.4 is non-polar and when it is higher than 1.5 it is ionic.
In our case, the electronegativity difference between O and B is 1.9, it seems that it would be an ionic bond. But that's not an option. The difference between H and B is 0.6, the polarity of that bond is weak compared to the polarity of the bond between O and B (if we consider that it is covalent).
So the answer to our problem is the first one:
BO₃ would have polar covalent bonds because