I think I'm getting an understanding of this topic now

<h2>Determining the Degree of Polynomials</h2>
<p>In this section, we will work with polynomials that have only one variable in each term. The degree of a polynomial and the degree of its terms are determined by the exponents of the variable.</p>
<p>A monomial that has no variable, just a constant, is a special case. The degree of a constant is \(0\)—it has no variable.</p>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Definition: Degree of a Polynomial</h3>
<p>The <strong>degree of a term</strong> is the exponent of its variable.</p>
<p>The <strong>degree of a constant</strong> is \(0.\)</p>
<p>The <strong>degree of a polynomial</strong> is the highest degree of all its terms.</p>
</div>
</div>
<p>Let's see how this works by looking at several polynomials. We'll take it step by step, starting with monomials, and then progressing to polynomials with more terms.</p>
<p>Remember: Any base written without an exponent has an implied exponent of \(1.\)</p>
<p><img alt="A table is shown. The top row is titled “Monomials” and lists the following monomials: 5, 4 b squared, negative 9 x cubed, negative 18. The next row is titled “Degree” and lists, in blue, 0, 2, 3, and 0. The next row is titled “Binomial” and lists the following binomials: b plus 1, 3a minus 7, y squared minus 9, 17 x cubed plus 14 x squared. The next row is titled “Degree of each term,” with “term” written in blue. This row lists 1, 0, 1, 0, 2, 0, 3, 2 in blue. The next row is titled “Degree of polynomial,” with “polynomial” written in red. This row lists 1, 1, 2, 3 in red. The next row is titled “Trinomial” and lists the following trinomials: x squared minus 5x plus 6, 4 y squared minus 7y plus 2, 5 a to the fourth minus 3 a cubed plus a, and x to the fourth plus 2 x squared minus 5. The next row is titled “Degree of each term,” with “term” written in blue. This row lists 2, 1, 0, 2, 1, 0, 4, 3, 1, 4, 2, 0 in blue. The next row is titled “Degree of polynomial,” with “polynomial” written in red. This row lists 2, 2, 4, 4 in red. The next row is titled “Polynomial” and lists the following polynomials: b plus 1, 4 y squared minus 7y plus 2, and 4 x to the fourth plus x cubed plus 8 x squared minus 9x plus 1. The next row is titled “Degree of each term,” with “term” written in blue. This row lists 1, 0, 2, 1, 0, 4, 3, 2, 1, 0 in blue. The next row is titled “Degree of polynomial,” with “polynomial” written in red. This row lists 1, 2, 4 in red." src="https://data.ulearngo.com/assets/73c01b5b-e26c-4faa-abb7-4b2527818aad"/></p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Find the degree of the following polynomials:</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}4x\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}3{x}^{3}-5x+7\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}-11\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}-6{x}^{2}+9x-3\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}8x+2\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td> </td>
<td>\(4x\)</td>
</tr>
<tr>
<td>The exponent of \(x\) is one. \(x={x}^{1}\)</td>
<td>The degree is 1.</td>
</tr>
<tr>
<td> </td>
<td>\(3{x}^{3}-5x+7\)</td>
</tr>
<tr>
<td>The highest degree of all the terms is 3.</td>
<td>The degree is 3</td>
</tr>
<tr>
<td> </td>
<td>\(-11\)</td>
</tr>
<tr>
<td>The degree of a constant is 0.</td>
<td>The degree is 0.</td>
</tr>
<tr>
<td> </td>
<td>\(-6{x}^{2}+9x-3\)</td>
</tr>
<tr>
<td>The highest degree of all the terms is 2.</td>
<td>The degree is 2.</td>
</tr>
<tr>
<td> </td>
<td>\(8x+2\)</td>
</tr>
<tr>
<td>The highest degree of all the terms is 1.</td>
<td>The degree is 1.</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<p>Working with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in <strong>standard form</strong>. Look back at the polynomials in the example above. Notice that they are all written in standard form. Get in the habit of writing the term with the highest degree first.</p>

77e14597-4d58-4399-be3f-b1bb5c28bc54

Determining the Degree of Polynomials

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Discover how to identify, determine the degree of, add, subtract, multiply, divide, and factor polynomials while also simplifying expressions with exponents in this tutorial.


Determining the Degree of Polynomials

Track Your Learning Progress

Earlier discussion