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?

1 Answer
George C.
Feb 19, 2018

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.

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