Math (Algebra) Question

Okay, I'm no math genius... more like a fucking math retard, but can someone explain this to me?

Ok, why is the degree of a variable with no exponent 1, and the degree of an actual number is 0?

I understand that they have to be those degrees to correctly multiply/divide polynomials, but how exactly did they prove that x = x^1 and 2 = 2^0 (Or any number for that matter...) And any number, to the power of 0 --

-- Ahh, while typing this I think I figured it out. Well, part of it anyway. Correct me if I'm wrong:

Numbers aren't to the power of 0, they have a null power, any number to the power of 0 is 1...

Ok then does Degree = Exponent = Power ?

When stating a degree of a term in a polynomial, if it's a number and it has a degree of 0, it doesn't mean it's to the power of 0, it just means it has no degree?



Wow holy fucking confusing post. My bad guys

Okay, I'm no math genius... more like a fucking math retard, but can someone explain this to me? Ok, why is the degree of a variable with no exponent 1, and the degree of an actual number is 0? I understand that they have to be those degrees to correctly multiply/divide polynomials, but how exactly did they prove that x = x^1 and 2 = 2^0 (Or any number for that matter...) And any number, to the power of 0 -- -- Ahh, while typing this I think I figured it out. Well, part of it anyway. Correct me if I'm wrong: Numbers aren't to the power of 0, they have a null power, any number to the power of 0 is 1... Ok then does Degree = Exponent = Power ? When stating a degree of a term in a polynomial, if it's a number and it has a degree of 0, it doesn't mean it's to the power of 0, it just means it has no degree? Wow holy fucking confusing post. My bad guys

Basically you're stating the power of the variable. 2x^2 has a degree of 2 just the same a 4x^2 and x^2. 2x has a degree of 1 just like 4x and x. Numbers without variables essentially have "x^0" attached to them, since x^0 will always be 1 regardless of x.

So for this equation:

y = 2x^2 + 4x +3

You could rewrite it as:

y = 2x^2 + 4x^1 + 3x^0

Since x^1 = x and x^0=1

The first term has a degree of 2, the second a degree of 1, and the last a degree of 0.