Question

PLEASE HELP!

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:

$6x^2$

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

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