Explore the division algorithm for polynumbers in this 45-minute lecture from the MathFoundations series. Learn about natural numbers, integers, fractions, and rational numbers before delving into their polynomial counterparts. Discover two approaches to dividing integral polynumbers: one starting with lower order terms and another with higher order terms. Examine positive polynumbers, integral polynumbers, and rational polynumbers, and work through exercises to reinforce your understanding. Gain insights into the logical foundations of mathematics and explore the similarities between polynomial division and long division of ordinary numbers.