The speed at which house prices fall over the next few months could depend less on mortgage rates and Americans’ appetite for home buying than on how banks decide to manage the huge number of foreclosed homes they own or may take from delinquent borrowers in the near future. Unlike home owners, banks often are much quicker to slash prices to unload properties quickly. The upshot is that, the more homes being sold by lenders, the faster prices tend to fall. That pattern was clear over the past two years: Price declines that began four years ago accelerated rapidly in 2008 as banks dumped foreclosed properties at fire-sale prices. By January 2009, the share of distressed sales had soared to 45% of all sales nationally; it was even higher in hard-hit markets such as Phoenix, according to analysts at Barclays Capital.