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Binomals are the simplest version of two monomials. Therefore, these have a lot of effect on any type of simplification. For more info on the significance of simplification in the real world, see monomials and trinomials.

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Adding on to the axis of symmetry example, the vertex would be the major turning point where the direction of the line changes and heads the opposite direction. That's the most important part of the graph in the real world for either a good reason or bad reason. There could be significant improvement, or maybe a major decrease of something valuable.

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Identifying symmetry is extremely signifacant for a reason similar to the linear expression example given. In the case of symmetry and change, this would mean there was some dramatic change that went in the opposite direction. This represents more of a real world example because there could be a huge decrease but then comes a huge increase. It's very unpredictable.

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Linear expressions help keep track of an increase/decrease at a constant rate, It is a visual representation of change in order to determine things such as slope /rate of change. There are changes going on every day although they are not necessarily constant. It is still important to have some idea of how to graph the changes you see.

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Trinomials have 3 different terms that can be operated with another trinomial or just other terms. This is again, multi-step equations which requires you to combine like terms and simplify. In math and in general, it is important to simplify harder concepts so that others can understand.

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Using this type of standard form keeps everything organized and is much easier for someone to comprehend. As I have said in previous examples, using this type of organization can help not just with classifying numbers, but organizing and priortizing in daily life.

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Polynomial is a general term so for specific examples, please reference trinomials or monomials. Polynomials, however, are basically multi-step equations when you put them together. Polynomials would help one practice combining like terms and simplifying.

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Monomials are dealing with only one term which is usually the result of simplification. Identifying simplest terms is very useful when simplifying larger problems. It is important to know how much you need to simplify.

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This example would be similar to the degree of a monomial example. By finding the degree of a polynomial, you can organize your terms which helps with organizination in general.

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A degree of a monomial can help you organize the different terms by greatest-least value which can ultimately help you with ordering and classifying pretty much anything. This could be sorting numbers in math or prioritizing your schedule.

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Constants are solid numbers that are not multiplied by anything such as a variable. An example of a constant could be a y-intercept because it is just one solid value.

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the maximum or minimum point of a parabola

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Vertical line that intersects the vertex of a parabola. If the parabola is reflected across this line, it will match up perfectly on itself.

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a polynomial of degree 1

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sum or difference of three monomials (it has three unlike terms which cannot be combined)

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A polynomial is in standard form when the terms are ordered so that the degrees of the monomial terms decrease from left to right (descending order based on the degree of each monomial of the polynomial).

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a monomial or the sum or difference of monomials

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a real number, a variable, or a product of a real number and one or more variables with whole-number exponents

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the largest degree of the monomial terms of a polynomial

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the sum of the exponents of the variables

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a term that has no variable factor; has a degree of zero

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sum or difference of two monomials (it has two unlike terms which cannot be combined)