So, let’s start with the low-hanging fruit. What is a polynomial?  For starters, a Polynomial is a sentence for algebraic equations, something like this:

4xy+3x + 2x+2

It’s usually comprised of numbers, variables and exponents. A set of these is called a term, terms can help us identify what kind of algebraic equation it is.

3xy is a Monomial

5ab-3a is a Binomial

4vk-3k+v is a Trinomial

5cd-3x+4-y-12 is a Polynomial

Note that anything that has 4 or more terms is classified as a Polynomial.

 

Polynomials also have degrees, in simple terms the degree of a Polynomial is the largest exponent the Polynomial has.

() + () – () + ()

3                3             1        0

If there are two different variables, add them together to get the degree

If two exponents are both the largest, then the Degree is still the same.

 

Operating with Polynomials

Addition :

Adding Polynomials is as simple as it can get, add all like terms together to get the answer.

() + () =

 

Subtraction:

Subtracting Polynomials only requires you to flip anything to the right of the minus symbol, all negatives become positives and all positives become negative, afterwards add them as you would normally.

() – ( + 3)

() + ( -3) =

()

 

Multiplication:

Multiplying is quite easy, multiply all like terms together, but add the exponents up.

() =

 

Division:

Like multiplication, all you have to do is divide all like terms together, but subtract the exponents instead.

()=

 

A few tips I could share:

If there is a number outside of the bracket, then you need to distribute the number to everything inside the bracket

Likewise, if there’s an operation behind the number closest to the bracket, leave it as is and distribute the number to everything inside the bracket.

If you’re dealing with smaller polynomials, you can use algebra tiles.

 

Have as a large square

as a rectangle

and 1 as a small square

Color them in on one side

Flip them over to the clear side when using a negative

Use them as you like.