A **trinomial** is a polynomial expression with three terms. For example:

- 3x – 8 + 4x
^{2} - x
^{2}– 2 + 4x - 10x – 8x
^{3}+ 3

## How to Write a Trinomial in Standard Form

To write a trinomial in standard form, list the terms in order of degree (the exponent or sum of exponents in each term): highest to lowest, and left to right.

**Example 1**: write the trinomial 3x – 8 + 4x^{2} in standard form.

Step 1: Note the degree of each term. There are three terms:

- 3x = Degree of 1; when x is on its own, it’s to the first power but we usually don’t write that out,
- 8 = Degree of zero; constants are usually assigned a zero degree or no degree at all. Another way to think of this: there isn’t a variable there so the degree doesn’t exist and must be zero,
- 4x
^{2}= Degree of 2.

Step 2: Write the terms in order of degree (don’t forget to use the correct ± signs from the original expression):

4x^{2} + 3x – 8.

**Example 2:** Express (x – 5)^{2} as a trinomial in standard form.

Step 1: Write the expression as a trinomial by expanding (you can use Symbolab’s calculator to do this part):

(x – 5)^{2} = (x – 5)(x – 5) = x^{2} – 10x + 25.

The trinomial is on order of degree, so we don’t need to do any additional steps.

## What’s the Point of Writing Trinomials in Standard Form?

Writing a trinomial in standard form makes it easier to see the overall degree of the expression. For example, the expression 7x^{3} + 2x + 8x^{6} is not written in standard form, so it’s easy to make the mistake of thinking it’s a third degree trinomial (it’s actually a 6th degree). Writing expressions this way makes it easier to see very large and very small numbers.

Another reason to place expressions in standard form: if your trinomial is a linear equation, standard form makes it easier to find intercepts.