Fundamental theorem

The fundamental theorem is the idea that certain things can be broken down into smaller, simpler pieces. It's like a puzzle - when you first look at it, it might seem really complicated, but if you break it into smaller pieces, it becomes easier to solve.

In math, the fundamental theorem usually refers to two specific things: the fundamental theorem of calculus, and the fundamental theorem of algebra.

The fundamental theorem of calculus says that if you have a function that's changing over time, you can figure out how much it's changing by looking at its derivative. The derivative tells you how much the function is changing at any given moment. By adding up all the changes over a certain period of time, you can figure out the total change in the function.

The fundamental theorem of algebra, on the other hand, says that any non-constant polynomial can be broken down into smaller pieces called factors. In other words, if you have a really complicated math problem, you can simplify it by breaking it down into smaller, more manageable pieces.

Both of these ideas are really important in math, because they help us solve problems that might otherwise seem impossible. By breaking things down into smaller pieces, we can make complicated problems much simpler to solve.