A **polynomial in standard form** is written with the terms in order from highest degree, to lowest degree. For example, the polynomial 4x^{3} + 8x^{2} + 2x – 21 can be written in standard form as:

Generally, speaking, the standard form of a polynomial equation can be written as:

**c**

_{n}·x^{n}+ c_{n – 1}·x – 1^{n}+ … + c_{1}·x + c_{0}= 0In other words, set your polynomial equal to 0 and write the terms in descending order by degrees. Sometimes (depending on your professor) it’s okay to omit the “= 0” part of the equation. Usually the clue is in the wording of the question:

- If you are giving an equation already set equal to zero, then include “= 0” in your answer.
- If you are given an equation that doesn’t include “= 0”, it’s usually okay to omit it.

For example, 5 + 9x^{3} -2x = 0 written in standard form is

9x^{3} -2x + 5 = 0.

But p(x) = 5 + 9x^{3} -2x in standard from is

p(x) = 9x^{3} -2x + 5.

## Polynomial in Standard Form: A Few Rules

The variable *x* is always assigned a degree of 1 and a constant term is always assigned a degree of zero (the “degree” doesn’t exist for a constant as there is no variable). Degree 0 polynomials are sometimes called *constant polynomials* [1].

If you have **more than one variable in a term**, make sure to add all of the degrees up to get the correct degree. For example, 3x^{5} + 5x^{3}y + ^{4}y^{5}z^{2} is written as a polynomial in standard form as:

^{4}y^{5}z^{2} + 3x^{5} + 5x^{3}y.

**Example question:** Which of these polynomials is in standard form?

- 4 + 5x
- 5x + 3 – x
^{2} - -21x
^{5}+ 3x^{3}– 99.

**Solution**: The third expression (-21x^{5} + 3x^{3} – 99) is in standard form because it is written in order of degree,

**Example question #2:** Write the following polynomial in standard form and classify the expression by degree: 3x^{2} – 7x

**Solution**:

Step 1: Write the degree of each term:

- 3x
^{2}= 2nd degree - – 7x
4 = 4th degree - + 38 = zero degree
- + 4x = 1st degree.

Step 2: Reorder the terms by order of degree:

– 7x^{2} + 4x + 38.

## References

[1] Wortman, K. Polynomials in Two Variables.