Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `4x^2-3x^3+6x+7`?

Answer 1

The expression in standard form is `-3x^3 + 4x^2 + 6x + 7`.

There are 4 non-zero terms.

The degree is 3.

Explanation:

There are 4 terms. They are

1. `-3x^3`.
2. `4x^2`.
3. `6x`.
4. `7`.

A polynomial in standard form should meet the following criteria:

• It should be expressed as a sum of, powers of `x` (or any other variable used).

For example, this is in standard form

`x^2 - 4x + 3`,

not

`(x-1) * (x-3)`,

nor

`(x-2)^2 - 1`.

• The term with the highest power goes first.

For example, this is in standard form

`x^2 - 4x + 3`,

not

`3 - 4x + x^2`.

The polynomial `4x^2-3x^3+6x+7` is not in standard form, as the term `-3x^3` comes after the term `4x^2`. Exchanging the two terms will solve the problem. So it becomes `-3x^3+4x^2+6x+7`.

The degree of polynomial is the highest power throughout the polynomial.

Since the powers are in decreasing order for a polynomial, the degree would be the power of the first term, which is a.k.a. the leading term.

The first term is `-3x^color(red)(3)`. The degree is `color(red)(3)`.