Find the degree and determine whether the polynomial is a monomial a binomial or a trinomial x^2+y^2+z^2

Terms are separated by + or - signs. The degree of each term is the sum of the degrees of the variables in it. The degree of the expression is the maximum of those sums.

The three terms here each have one variable. The exponents of those variables are all 2, so the maximum degree is 2.

The degree of the polynomial is 2.

Kind

The prefixes "mono-", "bi-", and "tri-" respectively signify 1, 2, and 3. Here, there are 3 terms, so the appropriate description is trinomial.

msm555 msm555 · Answer 2 · 2024-01-05T01:56:01+01:00

Answer:

Degree : 2

Polynomial: trinomial

Step-by-step explanation:

The given expression is [tex]\sf x^2 + y^2 + z^2[/tex].

Degree:

The degree of a term in a polynomial is the sum of the exponents of the variables in that term. In this case, each term has an exponent of 2. The highest exponent among these terms is 2.

So, the degree of [tex]\sf x^2 + y^2 + z^2[/tex] is 2.

Classification:

A monomial is a polynomial with exactly one term. [tex]\sf x^2 + y^2 + z^2[/tex] has three terms, so it's not a monomial.

A binomial is a polynomial with exactly two terms. [tex]\sf x^2 + y^2 + z^2[/tex] has three terms, so it's not a binomial.

A trinomial is a polynomial with exactly three terms. [tex]\sf x^2 + y^2 + z^2[/tex] has three terms, so it is a trinomial.

Therefore, [tex]\sf x^2 + y^2 + z^2[/tex] is a trinomial of degree 2.