consider π(x)=(x-x₀)(x-x₁)(x-x₂)...(x-xₙ), then using mathematical induction prove that the (n+1)th derivate of π(x) is (n+1)!

Mrs. avila is buying a wallpaper border to go on all of her kitchen walls. she wants to buy 5 extra feet of wallpaper border than she needs to be sure she has enough. she buys 55.5 feet of the border. the store owner selling the border uses the width of mrs. avila's kitchen to determine that the length of her kitchen must be 14.5 feet.