Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `g^4 - 2g^3 - g^5`?

Answer 1

The expression `-g^5+g^4-2g^3` is a 5th degree polynomial

Explanation:

The standard form of a polynomial means that the order of degree, with the highest degree going first, and then the next highest, and so on and so forth...

So, we go from `g^4-2g^3-g^5` to `-g^5+g^4-2g^3`

This is the standard form of the polynomial. Now let's classify it

Classification by term:
We are actually classifying the expression by the number of terms. So, there are more than 3 terms (`-g^5+g^4-2g^3+0g^2+0g`), which means we call it a polynomial

Classification by degree:
Once the expression is in standard form, we just look at the leading term, and the degree. So, the degree in this polynomial is `g^5`, so `color(red)(5)`.

The expression `-g^5+g^4-2g^3` is a 5th degree polynomial