8-4 Polynomials


Before we begin, lets get some definitions out of the way.


Polynomial- a monomial or a sum of monomials.
Binomial- sum of two monomials.
Trinomial- the sum of three monomials.

Identifying polynomials

Summary:

A monomial or sum of monomials is called a polynomial. However, when you add two monomials, the sum is called a binomial. Lastly, a Trinomial is the sum of three monomials. Each separate part of a polynomial that is being added is called a term. For example, this is a polynomial term: 6x³ In this section, you will learn to identify polynomials, find the degree of the polynomial, and finally you will learn to arrange the terms of a polynomial in ascending and descending order.



LINK 1


LINK 2

Here is a helpful table:


Term

6x----------------- 6x+3z------------ 5x³+4r+9x------- 2x²+9x³+2x+3r-

Which kind?

Monomial

Binomial

Trinomial

Polynomial


How to find the degree of the polynomial

The degree of the polynomial is the greatest degree of any term in the polynomial.
To find the degree, you look at the degree of each polynomial, and the highest degree is the degree of the polynomial.
To find the degree of a monomial, you add up all the degrees.

Example:

polynomial degree
2x²+3z----------2
64x⁵m ----------6 - *this is a monomial, so you have to add up all the exponents*
x³+5m+8x²+7--- 3


Putting polynomials in ascending order
The goal of this exercise is to have the exponents arranged so that they are lined up front least to greatest.

Example:

3x³+8x+x⁵=
8x+3x³+x⁵

8x+3x³+x⁵ is the correct answer because the variable's exponents are arranged in chronological order.
remember: it does not matter about the number in the front, it just matters about the exponent.

4x-x⁴+3z³=
4x+3z³-x⁴

4x+3z³-x⁴ is the correct answer because the variable's exponents are arranged in ascending order.
remember: it does not matter about the number in the front, it just matters about the exponent.

Putting polynomials in descending order
Here we will be doing almost the same thing. The only difference is that the powers of x must go in descending order.

Example:

7x⁴+x²+3x⁷+x=
3x⁷+7x⁴+x²+x

3x⁷+7x⁴+x²+x is the correct answer because the variable's exponents are arranged in descending order.
remember: it does not matter about the number in the front, it just matters about the exponent.

3x³+x⁶=
x⁶+3x³

x⁶+3x³ is the correct answer because the variable's exponents are arranged in descending order.
remember: it does not matter about the number in the front, it just matters about the exponent.

Use these problems for practice on 8-4