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Fermat's Last Theorem

Fermat's claimed he can demonstrate that for $n>2$ the equation $x^n+y^n=z^n$ has no integer solution. Despite the equation seems so elementary, only after 350 year later Andrew Wiles proved this theorem.

How To Do Graph Transformations

There are basically three type of basic transformations:

Shifting vertically or horizontally
Stretching / compressing vertically or horizontally
Reflecting about the $x$ -axis or $y$ -axis

The video below will explain in detail how to perform these transformations in detail and how to use this knowledge to graph a complicated function based on the graph of the basic function

How To Solve Polynomial Inequalities

Here are the steps to solve polynomial inequalities:

Move everything to the left hand side to make your inequality looks like $p(x)<0$ (here the inequality symbol can also be $>,\leq$ or $\geq$ )
Find the zeros of $p(x)$ (by factoring if it is possible)
Plot the zeros on the number line and these zeros will divide the number line into several intervals
Pick a sample point on each interval and plugin it to $p(x)$
If after plugin you get $p(x)<0$ is true then the interval on the number line where your $x$ belong is part of the solution, otherwise the interval is not part of the solution

The videos below will guide you step by step to solve te polynomial inequalities using a concrete example