Question

Determine the degree of the polynomial:
–3.1ax^4+2.5ax+2ax^4+1.1ax^4–0.5ax–2ax

Answer 1

Degree = -1*

Explanation:

The degree of a polynomial is its greatest exponent among all its terms.

To begin we group equal terms and solve the sums.

`P (x) = -3.1ax ^ 4 + 2.5ax + 2ax ^ 4 + 1.1ax ^ 4-0.5ax-2ax\\P (x) = -3.1ax ^ 4 + 2ax ^ 4 + 1.1ax ^ 4 + 2.5ax - 0.5ax -2ax`

Resolving the sums we have to:

P (x) = 0

This polynomial is considered a null polynomial.

There are several opinions about the degree of a null polynomial.

Some books consider it as -infinity, others say it is not defined.

On the other hand, some assign a grade -1 by convention *

* [Hernandez Ruiperez, Daniel (1990). Linear algebra. Salamanca, Spain. Pag. 41]