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?

Feb 19, 2018

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

Explanation:

Given:

$6 x {y}^{2} + 4 {x}^{3} {y}^{8} + 9 {x}^{2}$

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

${\overbrace{6 x {y}^{2}}}^{1 + 2 = 3} + {\overbrace{4 {x}^{3} {y}^{8}}}^{3 + 8 = 11} + {\overbrace{9 {x}^{2}}}^{2}$

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

$4 {x}^{3} {y}^{8} + 6 x {y}^{2} + 9 {x}^{2}$

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.