The high-pressure areas at the poles must be due to:

dense, rising air

cold, rising air

warm, rising air

heavy, sinking air

The answer is: cold, rising air.

The high-pressure areas are at the poles due to the cold rising air. It's known that the cold air is more sense that the warm air because the warm gases molecules are more separated during the gas, is warm, which make it less dense than cold air.

Due to the form of our planet and the location of the poles, the cold air rises while the warm air down around the tropics and rise again to the poles (getting cold while it's getting closer to the poles).

High-pressure at poles is also caused because the solar radiation is higher at the equator than at the poles.

Have a nice day!