Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `7g-3g^+8g^2-4`?

Answer 1

In standard form, it is written as: `8g^2+ 4g -4`
The degree of the polynomial is `2`.
It is a trinomial.

Explanation:

`7g-3g+8g^2-4`

First see if there are any like terms and combine them, if any:

In the given polynomial, `7g` and `-3g` can be added,so:

`4g +8g^2-4`

The degree of a term is determined by the exponent of the variable in that term.

Now look at the degree of each term in the polynomial:
`4g` has a degree of 1,
`8g` has a degree of 2, and
`4` has a degree of 0.

Now write this polynomial in order of degree, highest to lowest:

`8g^2+ 4g -4` --------- this is the standard form of the polynomial.

The highest degree identifies the degree of the polynomial, i.e. `2`.
The number of terms in the polynomial are `3`, so it is a trinomial.