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A detailed tutorial on degrees of polynomials. Step by step tutorial including several examples of degrees of polynomials for reference.

The degree of a polynomial is the highest power found in it. For example, in your normal quadratic equation, the degree is two, because the highest power – the highest number found in an exponent – is a two. In other polynomials, the degree may be something different. No matter what order the variables and their powers are placed in, the degree is always the highest one. For example. the degree of x^2 + x + 7 is exactly the same as x + 7 + x^2.

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A detailed tutorial on seven different basic graphs. Step by step tutorial including several visual examples of seven different basic graphs for reference.

A lot of time in any math class is devoted to the subject of graphs and graphing. But forming a graph when you are only given an equation can be difficult – unless you have some basic graphs memorized. Once you have these seven graphs memorized, it is very easy to follow the patterns in the equation and and simply fix your basic graphs to fit these new requirements. The basic graphs are the most basic patterns that x can be found in on any function – this is x, x squared, and x cubed. There is also the absolute value of x, the  natural log of x, and the exponential function of x. The last one is one divided by x, which while not being a basic form of x, is a very important form.

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A detailed tutorial on the different inverse operations. Step by step tutorial including several examples of the different inverse operations for reference.

Inverse operations are operations that undo each other – for example, if you do something a problem, and then use the inverse operation, it should be like it never happened. Common inverse functions are addition and subtraction, multiplication and division, square roots and squaring, and logarithms and exponents.

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A detailed tutorial on how to identify subsets of a set. Step by step tutorial including several examples of how to find subsets in a set for reference.

Each set in set theory has a certain amount of subsets. There is an easy way figure out how many subsets a set has. Pretend that every element of a set is 2, and multiply them together. This will be your number of subsets. For example, if you have three elements, you will have 8 subsets, because 2 cubed (which is 2 to the power of 3, or 2 times 2 times 2) is equal to 8. Now that you have determined how many subsets there are, you have to figure out what they are. A subset is defined as any set containing all or part of a set. Two subsets are going to be the set itself, and an empty set. Sometimes they are your only subsets. Now, following the definition, a subset must be all possible sets. This means, sets of one element - one for each element in your set. In addition to that, you may have sets of two elements – one for each possible combination of elements in your set. This should be continued until you have reached the maximum number of elements in the set you atarted out with.

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A detailed tutorial on the definition of the index of a radical expression. Step by step tutorial including several examples of the index of a radical expression for reference.

A radical expression is what most people know as a square root. The number, variable, or expression inside the square root symbol is referred to as the radicand. What some of you may not realize is that not only are there square roots, there are cube roots, and several other types of roots. These are the exact opposite functions of the exponents. A square root should technically have a little number two on the outside left of the square root symbol. A cube root would have a three there – any number can go there. That is the index.

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A detailed tutorial on identifying the radicand. Step by step tutorial including several examples of how to identify the radicand for reference.

The radicand is associated with what we know as a square root. However, there is a common misconception that a radicand and a square root are the same thing, and they are not. A square root is the entire number – the square root symbol, the number inside, and whatever number it equals. A radicand is simply the number that is inside the square root symbol. For example, take the expression . In this expression, the radicand is ab + 2, because that is what we are taking the square root of.

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A detailed tutorial on the solving of problems using the binomial theorem. Stepby step tutorial including several examples of how to solve problems using the binomial theorem for reference.

The binomial theorem is something you should all be familiar with – it is the alternative to the F.O.I.L. technique. It is used when you are given a binomial that is raised to a power. The simplest version of it is expressed like this:

This can also be expressed as a factorial notation, in the form: