Polar bears maintain homeostasis in freezing cold weather primarily through a combination of adaptations, but in the context of your options, the most relevant ones are:
a. their metabolism speeds up to produce heat - This is true to some extent, as polar bears can increase their metabolic rate to generate more body heat when needed.
c. their thick fur retains heat - This is also correct; polar bears have a dense layer of fur that insulates them and helps to retain body heat.
Thus, both a and c are important mechanisms by which polar bears maintain their body temperature in cold environments. However, if you had to choose only one answer that best summarizes their ability to maintain homeostasis in extreme cold, it would be:
c. their thick fur retains heat.
Additionally, it's essential to note that polar bears have a thick layer of blubber under their skin that also contributes significantly to insulation and heat retention.