# Does 1 have a degree of 1 or 0?

1. Sep 28, 2013

### student34

Or is it both?

2. Sep 28, 2013

### Office_Shredder

Staff Emeritus
Degree as what? A polynomial?

3. Sep 28, 2013

### arildno

Does it matter?

For every real r, we have 1=1^r

4. Sep 28, 2013

### student34

yes, as a polynomial

5. Sep 28, 2013

### student34

oh yeah

6. Sep 28, 2013

### Office_Shredder

Staff Emeritus
It's a degree zero polynomial - if it was degree one it would have a variable term.

7. Sep 28, 2013

### arildno

a*z^0 is a zero'th degree monomial in z, a first degree monomial in "a".

8. Sep 28, 2013

### student34

Oh, so even though 5 has a power of 1, is it still considered a degree of 0?

9. Sep 28, 2013

### student34

Ok, but what degree polynomial is 0 then?

10. Sep 28, 2013

### arildno

Do you understand the concept of a variable?

11. Sep 28, 2013

### student34

I have grade 12 algebra and grade 12 calculus, but any meaning of a variable beyond those courses, I am not sure.

I found an answer to the degree of 0; apparently it's -∞, !?

12. Sep 28, 2013

### statdad

"I found an answer to the degree of 0; apparently it's -∞, !?"

No, you haven't. Constants are polynomials of degree 0.

What do you mean 12 grade algebra and 12 grade calculus''?

13. Sep 28, 2013

### student34

I found it in my notes from my first year math course in university.

You have "12" and "grade" switched around.

14. Sep 28, 2013

### eigenperson

Some people do consider the degree of the zero polynomial to be -∞, so as to preserve rules like deg fg = deg f + deg g.

15. Oct 3, 2013

### HallsofIvy

The degree of a polynomial, in variable x, is the highest power of x. We can write "1" as "$1x^0$" so "degree 0". The reason for the distinction between the '0' polynomial (degree $-\infty$) and the '1' (or any non-zero number) polynomial (degree 0) is that we could, theoretically, write 0 as "$0x^n$" for any n.

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