The guides to the other example are quit sufficient

<h2>Evaluating a Polynomial for a Given Value</h2>
<p>In <a data-page="9" href="https://app.ulearngo.com/tutorial/mathematics-102/">Mathematics 102</a>, we evaluated expressions. Since polynomials are expressions, we'll follow the same procedures to evaluate polynomials—substitute the given value for the variable into the polynomial, and then simplify.</p>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>Evaluate \(3{x}^{2}-9x+7\) when</p>
<ol type="1">
<li>\(\phantom{\rule{0.2em}{0ex}}x=3\)</li>
<li>\(\phantom{\rule{0.2em}{0ex}}x=-1\)</li>
</ol>
</div>
<div>
<h3>Solution</h3>
<table data-label="" summary=".">
<tbody>
<tr>
<td>\(x=3\)</td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(3{x}^{2}-9x+7\)</td>
</tr>
<tr>
<td>Substitute 3 for \(x\)</td>
<td>\(3{\left(3\right)}^{2}-9\left(3\right)+7\)</td>
</tr>
<tr>
<td>Simplify the expression with the exponent.</td>
<td>\(3·9-9\left(3\right)+7\)</td>
</tr>
<tr>
<td>Multiply.</td>
<td>\(27-27+7\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(7\)</td>
</tr>
</tbody>
</table>
<table data-label="" summary=".">
<tbody>
<tr>
<td>\(x=-1\)</td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(3{x}^{2}-9x+7\)</td>
</tr>
<tr>
<td>Substitute −1 for \(x\)</td>
<td>\(3{\left(-1\right)}^{2}-9\left(-1\right)+7\)</td>
</tr>
<tr>
<td>Simplify the expression with the exponent.</td>
<td>\(3·1-9\left(-1\right)+7\)</td>
</tr>
<tr>
<td>Multiply.</td>
<td>\(3+9+7\)</td>
</tr>
<tr>
<td>Simplify.</td>
<td>\(19\)</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>
<div class="ns-school-emp">
<h2>Example</h2>
<div class="ns-school-defn">
<div data-type="example">
<div>
<div>
<p>The polynomial \(-16{t}^{2}+300\) gives the height of an object \(t\) seconds after it is dropped from a \(300\) foot tall bridge. Find the height after \(t=3\) seconds.</p>
</div>
<div>
<h3>Solution</h3>
<table data-label="" style="width: 460px;" summary="The top line says negative 16 t squared plus 300. The next line says, “Substitute 3 for t,” and shows negative 16 times a red 3 squared plus 300. The next line says, “Simplify the expression with the exponent,” and shows negative 16 times 9 plus 300. The next line says, “Multiply,” and shows negative 144 plus 300. The next line says, “Simplify,” and shows 156. The last line says, “After 3 seconds, the height of the object is 156 feet.">
<tbody>
<tr>
<td style="width: 299px;"> </td>
<td style="width: 147px;"><img alt="." src="https://data.ulearngo.com/assets/8391343c-e0b6-41dd-82ca-74892262f81b"/></td>
</tr>
<tr>
<td style="width: 299px;">Substitute 3 for \(t\)</td>
<td style="width: 147px;"><img alt="." src="https://data.ulearngo.com/assets/0813cda5-38c6-47d0-8a53-23748f421b76"/></td>
</tr>
<tr>
<td style="width: 299px;">Simplify the expression with the exponent.</td>
<td style="width: 147px;"><img alt="." src="https://data.ulearngo.com/assets/50ea1b9b-f05f-4010-b579-7f6763daf48f"/></td>
</tr>
<tr>
<td style="width: 299px;">Multiply.</td>
<td style="width: 147px;"><img alt="." src="https://data.ulearngo.com/assets/7380f7e7-6ff7-4671-9d82-6ce284ac0e70"/></td>
</tr>
<tr>
<td style="width: 299px;">Simplify.</td>
<td style="width: 147px;"><img alt="." src="https://data.ulearngo.com/assets/7b3b09eb-f99e-4c5c-bba0-786c1e70d474"/></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
</div>

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Evaluating a Polynomial for a Given Value

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

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


Evaluating a Polynomial for a Given Value

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