<p><span style="font-size:22px"><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-polynomial-degree">Polynomial Degree Exercise</a></span></p><p>The degree of a polynomial is the highest power of the variable in the polynomial. Think of it as the head honcho, the top dog, the main event.</p>
<p>You can assign a degree to both a single term and an entire polynomial expression:</p>
<ul>
<li><strong>Degree of a Term:</strong> The sum of the exponents of the variables in that term:
<ul>
<li>Example: $6x^2y^3$ has a degree of $2 + 3 = 5$.</li>
</ul>
</li>
<li><strong>Degree of a Polynomial (Expression):</strong> The highest degree of any term in the polynomial:
<ul>
<li>Example: $5x^4 + 2x^2y - 7xy^2 + 4$ has a degree of $4$ because the first term has a degree of $4$, while the remaining terms have degrees of $3$, $3$, and $0$.</li>
</ul>
</li>
</ul>
<p>Some other notes:</p>
<p>- A constant has a degree of $0$ - For example, you can re-write $8$ as $8x^0$ (remember that variables raised to the power of $0$ would be $1$)<br />
- You sum up the exponents, even if they come from different variables - In the case of $x^2y^2 + x^3$ , the degree is actually $4$, not $3$.</p>
<p>So, keep an eye on those exponents—they’re the ones running the show!</p>