Math 08

Polynomials

This is my essay for 8th grade math lesson 46:   

Definition of a Polynomial

Polynomial:  An expression that has no operations other than addition, subtraction, and multiplication by or of the variables.  

Here are some examples of polynomials:

5x – 3x3 + 7

8x4 – 11x2 + 2x5 – x2 + 4

5x7 + 9x4 – 3x2 + 8 

x – 1

x2 + 3

These are NOT polynomials:

3x + 2/9x   This is not a polynomial because the fraction line means that there is a division taking place, and division is not an operation approved of by the polynomial definition shown above.

|4x2 – 1|   This cannot be a polynomial because absolute value is not a function approved of by the definition either.

Parts of a Polynomial

6x2

The 6 would be called the coefficient, the x would be called the variable, and the would be called the exponent.

Degree of Polynomials

The degree of a polynomial is just the largest exponent.  Example:

9x5 + 3x2 + 9  This is a fifth degree polynomial, because the largest exponent is 5.

Naming a Polynomial

Naming a polynomial is easy.  Some polynomials have special names, according to their degree and by how many terms they have.  I will show you how to name them by the number of terms they have first:

5x   This is called a Monomial.  It has one term.

8y – 2   This is a Binomial.  It has two terms.

4y2 + 3y + 1   This is  a Trinomial. It has three terms.

The best I can word it is: a term is the numbers and/or variables and exponents that are separated by the addition and subtraction symbols.

Here is how to name them by their degrees:

9x – 2   This is a linear binomial.  It’s called linear because the highest power is 1. (The one isn’t shown, but it is implied).

4y2 + 3y + 1   This is a quadratic trinomial. It’s called quadratic because the highest power is 2.

5y3   This is a cubic monomial.  It’s called cubic because it’s highest power is 3.

Those are the polynomials that have special names. The ones that have over three terms or powers are named like this:

5x7 + 3x2 + x + 9   This is a 7th order polynomial with 4 terms.

I hope you found this essay helpful! Thanks for reading, and if you like this essay and some of my other ones, please follow me! I would appreciate it so much I would follow you back!

Love, Caitlin📝

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