What is a polynomial?
A grammatical construction expression of more than two algebraic terms, especially the sum of several terms that contain different business leaders of the same variable. To clarify it is when you have two separate expressions with multiple algebraic terms. An algebraic term is a term used for involving or repeating a finite number while adding an addition sign, subtraction sign, division sign, multiplication sign, comparing sign, extracting roots and/or using powers.
Vocabulary
Some vocabulary that is used to understand the language of polynomials is degree, constant, coefficient, leading coefficient, binomial, trinomial and a monomial. You are probably wondering what those are or just confused in general! It’s ok! I will explain. Starting with a degree, a degree is a term used to describe the highest/biggest/strongest variable in the equation, for example, x2-2x-4=0 this equation would be considered full with a degree. A constant is the one number that stays the same (is always constant/never changes). An example would be 4x-7=5, 7 being the constant (because it stayed consistent). A coefficient is a constant quantity that is placed before they multiple or is the variable placed before an algebraic expression, an example is 4 in 4xy. A leading coefficient is when there are more than one coefficients, to be the leading coefficient you have to have a higher quantity than the other coefficient(s), an example, -7x4+2x3-11 in this situation -7 would be the leading coefficient. A binomial is a term used to describe a consisting of two terms, comparable to the sum of two different expressions, an example of a simple expression would be “a+b”. A trinomial is related to binomial however the tri stands for three which just means it is three algebraic terms, an example “a+b+c”. A monomial is a minimum of the two (binomial/trinomial) it consists of one algebraic term for example “a”.
What are algebra tiles and how to use them
These here are algebra tiles! 
They are a great visual way to simplify and solve algebraic expressions, however, they can only go so far. We might as well use them while we can. Some situations were we could not use them would be, too many numbers (don’t have enough tiles), there is more than one letter (instead of “x” “y”), too complicated or too big of an equation.
The colorful side is considered a positive side and the white side is negative!
Each different size of the square stands for a different number or expression.
Example of an equation (4x-(-6×2)+2×2):
Step one: organize biggest to smallest:
Step two: cancel the pairs:
Step three: write ur new, simplified equation down (-4×2+4x) :
Adding and subtracting polynomials
Before starting adding or subtracting polynomials you have you analyze to see how many different variables there are and what type there are, afterward grouping them! Anything else that you can possibly see to make it easier to simplify the equation from the beginning. In addition, you would then proceed by adding the variables and reorganizing them biggest to the smallest left to right (consider it like the alphabet but numbers). In view of subtraction, you would proceed in a very similar way as addition just by subtracting the variables and again reorganizing the mathematical way.
Multiplying and dividing polynomials
Multiplication and division are quite simple, in fact, it is ur normal multiplication 2×3=6 or division 6÷2+3. There is a twist! There are variables, exponent, and coefficients. Multiplication would be the norm 2×3=6, however, if we add an “x” then you would have a different answer, an example, 2x multiplied by 3x would be 6×2! But how?! imagine that “x” = 1, when adding 1+1=2, the same thing with “x” except the “x” always stays! The division is similar yet different. The division is considered the same as multiplication just direct opposites. A normal number 4 can be divided by 2 easily. When adding in “x” you would have “x” stick around for as long as possible! Here is an example, 4x divided by 2 is 2x, simple!
Making connections to previous units
In my eyes, I feel that the biggest connection would be exponents for specifically power laws. Power laws are what ties in the most from previous units and are used the exact same way in multiplication and division as in previous units!