Respuesta :
Degree of polynomials:
[tex]6x^2 = 2\\\\18x^3+5ab-6y = 3\\\\4x^3y +3x^2-xy-4 = 4\\[/tex]
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
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
[tex]6x^2[/tex]
Here the highest degree is 2 ( x power 2)
In this case, degree of polynomial is 2
Option II
[tex]18x^3+5ab-6y[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]Degree\ of\ 18x^3 = 3[/tex]
[tex]Degree\ of\ 5ab = 5a^1b^1 = 1+1 = 2[/tex]
[tex]Degree\ of\ 6y = 6y^1 = 1[/tex]
Thus the highest degree is 3
Option III
[tex]8a^{-5}[/tex]
This is not a polynomial
A polynomial does not contain variables raised to negative
Option IV
[tex]4x^3y +3x^2-xy-4[/tex]
To find the degree of the polynomial, add up the exponents of each term and select the highest sum.
[tex]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[/tex]
Thus highest degree is 4
Then organize the expressions from least to greatest based on their degree
Least to greatest based on degree:
[tex]6x^2[/tex]
[tex]18x^3+5ab-6y[/tex]
[tex]4x^3y +3x^2-xy-4[/tex]
