Pure: Polynomials

A. Factorial (n!) Definition: The factorial of a non-negative integer 'n', denoted by n!, is the product of all positive integers less than or equal to 'n'. By definition, 0! is equal to 1. Explanation: Factorials are a mathematical operation that helps us count the number of ways to arrange 'n' distinct items in a sequence. For example, 3! means 3 × 2 × 1 = 6. It tells us there are 6 different ways to arrange 3 distinct items. The special case 0! = 1 is crucial for formulas to work consistently in permutations and combinations. Think of it as: Imagine you have 'n' different books. 'n!' represents all the different ways you can arrange these books on a shelf, considering each arrangement as unique. Real-world application: Factorials are used in probability calculations, determining the number of possible arrangements of items (e.g., how many ways 5 people can sit in 5 chairs), and form the basis for many formulas in statistics and combinatorics. B.