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

Mar 6, 2016

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

There are 4 non-zero terms.

The degree is 3.

Explanation:

There are 4 terms. They are

1. $- 3 {x}^{3}$.
2. $4 {x}^{2}$.
3. $6 x$.
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

${x}^{2} - 4 x + 3$,

not

$\left(x - 1\right) \cdot \left(x - 3\right)$,

nor

${\left(x - 2\right)}^{2} - 1$.

• The term with the highest power goes first.

For example, this is in standard form

${x}^{2} - 4 x + 3$,

not

$3 - 4 x + {x}^{2}$.

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

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 $- 3 {x}^{\textcolor{red}{3}}$. The degree is $\textcolor{red}{3}$.