What is the order of decreasing degree?

Answer 1

Order of Decreasing Degree means that your polynomial is ordered from greatest to least, based on exponents, or degrees.

Ex. 1 -12x^2+36y^3, because Y has a greater exponent (3) it goes first in order of decreasing degree.

But when you have multiple variables each with it's own exponent, something different happens.

Ex. 2 -12x^3y^3+36x^2y^2

You must add the exponents in each part together to get the final degree.

(cont.) The degree of the first part is 6, because when the exponents of x^3 and y^3 are added they equal six. The degree of the second part is 4, because when the exponents of x^2 and y^2 are added they equal 4. So the degree of -12x^3y^3 is 6 and the degree of 36x^2y^2 is 4. When we order the degrees 6 and 4 from greatest to least, we see 6 comes first, there fore the equation -12x^3y^3+36x^2y^2 was already arranged in order of decreasing degree.

Now then, when you have an equation like -6x^3+32x^2y+30xy^2+4y^3 where all the degrees are the same (remember above a single variable, like x, there is an imaginary exponent of 1) I'm not sure if it matters what order they are in, and it would be worth looking elsewhere to see.