Factorial
Calculate n factorial as the product of all positive integers from 1 to n. Use factorials to compute permutations and combinations in Grade 9 probability.
Key Concepts
Property The factorial $n!$ is defined for any natural number $n$ as $n! = n(n 1)...(2)(1)$. Zero factorial is defined to be 1. $0! = 1$. Explanation Factorials are all about arranging things in a line. If you have 'n' items, you have 'n' choices for the first spot, then 'n 1' for the second, and so on down to one. It's like a countdown multiplication party! It’s the perfect tool for calculating the total number of ways to order an entire group. Examples To find the value of five factorial, you multiply all whole numbers from 5 down to 1: $5! = 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 120$. To simplify a factorial fraction, cancel out the common parts: $\frac{8!}{5!} = \frac{8 \cdot 7 \cdot 6 \cdot 5!}{5!} = 8 \cdot 7 \cdot 6 = 336$. The number of ways 4 friends can stand in a line for a photo is $4! = 4 \cdot 3 \cdot 2 \cdot 1 = 24$ ways.
Common Questions
What is the first step when factorial?
Always check for a greatest common factor (GCF) first. Factor out the GCF before applying grouping or special product patterns.
How do you verify factoring is correct?
Multiply your factors back together using distribution. If the product matches the original polynomial exactly, the factoring is correct.
When is factoring used in algebra?
Factoring solves quadratic equations, simplifies rational expressions, and finds zeros of polynomial functions in Grade 9 algebra.