Question

PLEASE HELP!

First determine the degree of each polynomial expression below. Explain how you determined this on each expression.Then organize the expressions from least to greatest based on their degree
I. 6x^2
II. 18x^3+5ab-6y
III.8a-5
IV. 4x^3y+3x^2-xy-4​

Answer 1

Degree of polynomials:

`6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\`

Least to greatest based on degree:

`6x^2`

`18x^3+5ab-6y`

`4x^3y +3x^2-xy-4`

Solution:

The degree of the polynomial is the highest degree of any of the terms

Know that the degree of a constant is zero

Option I

`6x^2`

Here the highest degree is 2 ( x power 2)

In this case, degree of polynomial is 2

Option II

`18x^3+5ab-6y`

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

`Degree\ of\ 18x^3 = 3`

`Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2`

`Degree\ of\ 6y = 6y^1 = 1`

Thus the highest degree is 3

Option III

`8a^(-5)`

This is not a polynomial

A polynomial does not contain variables raised to negative

Option IV

`4x^3y +3x^2-xy-4`

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

`Degree\ of\ 4x^3y = 4x^3y^1=3+1 = 4\\\\Degree\ of\ 3x^2 = 2\\\\Degree\ of\ xy = x^1y^1 = 1+1 = 2\\\\Degree\ of\ 4 = 0`

Thus highest degree is 4

Then organize the expressions from least to greatest based on their degree

Least to greatest based on degree:

`6x^2`

`18x^3+5ab-6y`

`4x^3y +3x^2-xy-4`