Author:
Sara Gorsuch

To create and understand of what Polynomials are, and what to do with them!

I show what polynomials are, how to define them in various ways and even what types of jobs use them. Also, going through simplifying them using addition and subtraction and multiplication!

Tutorial

Polynomial: is just an expression that has a bunch of variable or constant terms in them that are raised to non-zero exponents.

**Remember:** No polynomial has a negative or fractional exponent or a root sign within the expression, if it does it is NOT a polynomial.

Polynomial Termonology:

__ Degree:__ This is the highest exponent in the polynomial, look to the highest exponent and that will define the degree of the polynomial.

Example: 4x^{4}+5x^{2}=18 as you see in this expression the highest exponent is a 4th, so the polynomial would be defined as a 4th degree polynomial.

(eventually in polynomials you will want to find what x is, the degrees will eventually tell you how many answers there are to x, so if there is for example 4x^{2}+8x+25 there will be two values for x)

** Standard Form Polynomial:** With a polynomial the standard form is when the expression is put in order from the largest to the smallest exponents, then to basic variables and then to the constants(numbers)

Example: 5x^{8}+3x^{4}-7x+4 this is standard form because as you see, first is the largest exponent then the next largest, next the basic variable and then the constant(number).

What do you do with polynomials? Well, you need to learn how to simplify them using multiplication, addition, subtracting and division. This will lead into factoring them and solving for x. Also, a bit of graphing.

**Who even uses polynomials in real life? What kind of jobs use this stuff?**

Fields relating to architecture, agriculture, engineering fields such as electrical and civil engineering and various other science related jobs. Even people with regular business jobs use polynomials! It is even used in our regular finances!