Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `6xy^2 + 4x^3y^8 + 9x^2`?

Answer 1

This is an undecic (degree `11`) trinomial polynomial in two variables.

Explanation:

Given:

`6xy^2+4x^3y^8+9x^2`

The degree of each term is the sum of the degrees of the variables:

`overbrace(6xy^2)^(1+2=3) + overbrace(4x^3y^8)^(3+8=11) + overbrace(9x^2)^2`

To put the polynomial in standard form, reorder the terms in descending order of degree to get:

`4x^3y^8+6xy^2+9x^2`

The degree of the polynomial is the highest degree of any term, so `11` in this example.

We do not usually use a special name for polynomial of degree `11`, but if we did it would probably be called an undecic or possibly hendecic polynomial.

Since there are three terms, this is also called a trinomial.