Pascal’s Triangle is a great example of a non-linear pattern that has applications in the world of algebra and equations. The numbers from each row can be used when factoring polynomials. The triangle is formed in the following way.
The outside edges of the triangle are made up of ones that form an isosceles triangle. The apex of the triangle is based on the concept of raising a variable to the zero power. Since anything raised to the zero power is one, the number one is placed at the top of the triangle and we call this the “row zero.” Within the outside edges, the individual numbers are found by taking the sum of two numbers directly above it. These numbers form symmetrical rows that read the same forward and backward.
When using this triangle, the numbers in each row represent the coefficients when a polynomial is raised to the power that corresponds to the number of that row. For instance, row four reads “1, 4, 6, 4, 1.” This means that if you are multiplying the polynomial (x + y)4, you would get the following polynomial:
x4 + 4×3y + 6×2y2 + 4xy3 + y4
