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A detailed tutorial on how to use algebra tiles. Step by step tutorial including several examples of how to use algebra tiles for reference.

Algebra tiles are a visual expression of polynomials and polynomial equations. Each tile is meant to represent a different polynomial. A large square tile represents the squared variable, a smaller square tile represents a single number, with no variable, and a rectangle represents the single variable. The tiles are red and green. Green represents positive monomials, and red represents negative monomials. Tiles can be combined to create equations, or the same tiles can be combined to express the coefficient. Addition and subtraction can be performed by adding and removing tiles.

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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 identifying zero polynomials. Step by step tutorial including several examples of identifying zero polynomials for reference.

A zero polynomial is the additive identity of an additive group of polynomials. So this means it is not a unique polynomial, even though it may seem like it. In order to identify a zero polynomial, you need to be aware of the two properties that zero polynomials possess. The first one is that all coefficients of a zero polynomial are zero, and add up to zero. The second is that a zero polynomial doesn’t have a degree – it is an undefined degree. Typically people will write this as a degree of -1, or more common, of negative infinity.

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A detailed tutorial on polynomial long division. Step by step tutorial including several examples of polynomial long division for reference.

Polynomial long division is a mix of regular long division and rules of polynomials – it looks confusing at first, but isn’t too difficult to follow. Polynomial long division is actually a type of algorithm. It is only used when dividing a polynomial by another polynomial of either the same or a lower degree. The “degree” of a polynomial is the highest power in the polynomial, and the terms in the polynomial should be ordered from highest degree to lowest degree. When using polynomial long division, you must write out all coefficients and terms, even “invisible” ones – ones that have a coefficient of zero and so are typically not written in the polynomial. Polynomial long division is solved the same way as regular long division

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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: