Question

please someone can Tell me whether the expression is a polynomial. If it is, give its degree.

-2\pi
Choose the right answer right.
a. polynomial, degree -2
b. not a polynomial
c. polynomial, degree 1
d. polynomial, degree 0

Answer 1

What is the right answer?

Answer 2

A polynominal is a (finite) sum of monomials.

A monomial is term like
\[ax^n, \ \ \ \text{ where a is a constant and n is zero or a positive integer}\]
examples of monomials are
1, 5, 2x, -17x, pi.x^2, (17-pi).x^3, x^1777444, -10^20.x^20

Answer 3

The degree of a polynominal is defined to be the highest index of the monomials that make up the polynominal.

Hence x^2 + 1 is of degree 2
Degree 1: -17x
Degree 1: 5x - 15
Degree 0: 0
Degree 0: 15
Degree 3: x^3 - x^2 + 2x - 50000
Degree 3: 50000x^3 + 1

Answer 4

So given all that, is
\[-2\pi\]
a polynominal and what is its degree?

Answer 5

I think it is -2

Answer 6

If the degree were -2 there would be a term x^{-2} somewhere, but there isn't. So -2 can't be the answer.

In fact, if you look carefully at how we defined monomials, we can't ever have negative indices on the variable. And therefore degree is also never negative. The degree of a polynominal is also zero or a positive integer.