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<p class="os-raise-text-bold os-raise-text-italicize">The following information can be shared with students' families to help support student engagement and encouragement at home.</p>
<div class="os-raise-familysupport">
<p><a href="https://k12.openstax.org/contents/raise/resources/f5a18c23e197d3620a9132512b3d7436e454f292" target="_blank">Access the PDF version</a> of this page to share with parents or guardians. <a href="https://k12.openstax.org/contents/raise/resources/348b652977e38a8c3a49bf25622cd9dfdd98ab92" target="_blank"> Spanish version available.</a></p>
</div>
<h4>Working with Polynomials</h4>
<p>In this unit, your student will learn that a monomial is an algebraic expression with exactly one term. A polynomial is a monomial (one term) or a combination of monomials (two or more terms). When there is more than one monomial term, the terms are separated by addition or subtraction.You can classify a polynomial by the number of terms and by the degree, which is the value of the highest power of the variable of its individual terms. </p>
<table class="os-raise-doubleheadertable">
<caption>
Classifying polynomials by the number of terms and degree of the polynomial
</caption>
<thead>
<tr>
<th scope="col"></th>
<th scope="col">Monomial</th>
<th scope="col">Binomial</th>
<th scope="col">Trinomial</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">Example</th>
<td>\(5x^2\)</td>
<td>\(4x + 6y\)</td>
<td>\(3x^2 + 8y^3 - z\)</td>
</tr>
<tr>
<th scope="row">Term (s)</th>
<td>Exactly 1</td>
<td>Exactly 2</td>
<td>Exactly 3</td>
</tr>
<tr>
<th scope="row">Highest power of the variable</th>
<td>2</td>
<td>1</td>
<td>3</td>
</tr>
</tbody>
</table>
<br>
<p class="os-raise-text-bold">Adding or subtracting polynomials by combining like terms.</p>
<p>"Like terms" are monomials that contain matching variables that have the same exponent. </p>
<br>
<ol class="os-raise-noindent">
<li> \((3k^2+6k+2)+(9k^2-7k-4)\)</li>
</ol>
<p> <strong>Step 1 -</strong> Use commutative property to rearrange like terms and then use the associative property to regroup.</p>
<p>\((3k^2+9k^2)+(6k-7k)+(2-4)\)</p>
<p> <strong>Step 2 - </strong>Combine like terms.</p>
<p> \( 12k^2-k-2\)</p>
<br>
<ol class="os-raise-noindent" start="2">
<li> \((3x^2+7xy-3y^2)-(5x^2-4y^2)\)</li>
</ol>
<p> <strong>Step 1 - </strong> Use the distributive property to remove parentheses from the subtracted terms.</p>
<p> \((3x^2+7xy-3y^2)-5x^2+4y^2\)</p>
<p> <strong>Step 2 - </strong> Use the commutative property to move like terms and then the associative property to regroup them.</p>
<p> \((3x^2-5x^2)+7xy+(-3y^2+4y^2)\)</p>
<p> <strong>Step 3 - </strong> Combine like terms.</p>
<p> \(-2x^2+7xy+y^2\)</p>
<p class="os-raise-text-bold">Multiplying polynomials by using the distributive property</p>
<p>The “distributive property” multiplies a factor to every term contained within parentheses.</p>
<br>
<ol class="os-raise-noindent">
<li> \(2(p+6)\)</li>
</ol>
<p> <strong>Step 1 - </strong> Use the distributive property to multiply 2 by each term in parentheses.</p>
<p> \(2p+2 \cdot 6\)</p>
<p> <strong>Step 2 - </strong> Multiply.</p>
<p> \(2p+12\)</p>
<br>
<ol class="os-raise-noindent" start="2">
<li>\(6x(x-5)\)</li>
</ol>
<p> <strong>Step 1 - </strong> Use the distributive property to multiply 6x by each term in parentheses.</p>
<p> \(6x \cdot x-6x \cdot 5\)</p>
<p> <strong>Step 2 - </strong> Use the commutative property to rearrange factors.<br>
</p>
<p> \(6x \cdot x-6 \cdot 5 \cdot x\)</p>
<p> <strong>Step 3 - </strong> Multiply. Use the property of exponents to multiply \(x^1 \cdot x^1=x^2\).</p>
<p> \(6x^2-30x\)</p>
<h3>Apply</h3>
<p class="os-raise-text-bold">Try this with your student.</p>
<p>A rectangular garden plot has a length that can be expressed as \(x + 5\) feet and a width expressed as \(x\) feet.</p>
<p><img alt="rectangle labeled as shown" class="img-fluid atto_image_button_text-bottom" height="107" src="https://k12.openstax.org/contents/raise/resources/282cfe00545c266e4531385b3a5db25f59bc3e81" width="208"></p>
<p class="os-raise-text-bold">Complete the following questions. </p>
<ol class="os-raise-noindent">
<li> Write a polynomial expression to represent the perimeter of the garden. </li>
<li> Write a polynomial expression to represent the area of the garden. </li>
<li> What is the perimeter if \(x = 15\)? </li>
<li> What is the area of \(x = 15\)? </li>
</ol>
<p class="os-raise-text-bold">Hide the answers until you have attempted the questions.</p>
<ol class="os-raise-noindent">
<li> The perimeter of a rectangle is the sum of its side lengths, \(2 \cdot length + 2 \cdot width\)</li>
</ol>
<p> <strong>Step 1 - </strong> Substitute the length and width into the expression for perimeter.</p>
<p> \(2(x+5)+2(x)\)</p>
<p> <strong>Step 2 - </strong>Use the distributive property to multiply \(2\) by each term in parentheses.</p>
<p> \(2 \cdot x+2 \cdot 5+2(x)\)</p>
<p> <strong>Step 3 - </strong>Multiply.</p>
<p> \(2x+10+2x\) </p>
<p> <strong>Step 4 - </strong> Use the commutative property to gather like terms and combine them.</p>
<p> \(2x+2x+10\)</p>
<p> \(4x+10\)</p>
<p><strong>Step 5 - </strong> Write out your answer. The perimeter is \(4x+10\) feet.</p>
<br>
<ol class="os-raise-noindent" start="2">
<li> The area of a rectangle is \(length \cdot width\).</li>
</ol>
<p> <strong>Step 1 - </strong>Substitute the length and width into the expression for area.</p>
<p> \((x+5)(x)\)</p>
<p> <strong>Step 2 - </strong> Use the distributive property to multiply \(x\) by each term in parentheses.</p>
<p> \((x \cdot x)+(5 \cdot x)\)</p>
<p> <strong>Step 3 - </strong> Multiply.</p>
<p> \(x^2+5x\)</p>
<p> <strong>Step 4 - </strong> Write out your answer (there are no like terms to combine). The area is \((x^2+5x)\) square feet.</p>
<br>
<ol class="os-raise-noindent" start="3">
<li>The expression for perimeter is \(4x+10\).</li>
</ol>
<p> <strong>Step 1 - </strong> Substitute \(15\) for \(x\) into the expression for perimeter.</p>
<p> \(4(15)+10\)</p>
<p> <strong>Step 2 - </strong> Multply.</p>
<p> \(60 + 10\)</p>
<p> <strong>Step 3 - </strong> Add.</p>
<p> \(70\)</p>
<p> <strong>Step 4 - </strong> Write out your answer. The perimeter is \(70\) feet.</p>
<br>
<ol class="os-raise-noindent" start="4">
<li>The expression for area is \(x^2+5x\).</li>
</ol>
<p> <strong>Step 1 - </strong>Substitute \(15\) for \(x\) into the expression for area.</p>
<p> \((15)^2+5(15)\)</p>
<p> <strong>Step 2 - </strong>Evaluate the exponent and multiply.</p>
<p>\(225+75\)</p>
<p><strong>Step 3 - </strong> Add.</p>
<p> \(300\).</p>
<p><strong>Step 4 - </strong> Write out your answer. The area is \(300\) square feet.</p>
<h3>Review</h3>
<p class="os-raise-text-bold">Video lesson summaries for Unit 6 - Working with Polynomials</p>
<p>Each video highlights key concepts and vocabulary that students learn across each lesson in the unit. The goal of these videos is to support students in reviewing and checking their understanding of important concepts and vocabulary. </p>
<p class="os-raise-text-bold">Here are some possible ways families can use these videos.</p>
<ul>
<li>Keep informed on concepts and vocabulary students are learning about in class.</li>
<li>Watch with their students and pause at key points to predict what comes next or think up other examples of vocabulary terms.</li>
</ul>
<table class="os-raise-textheavytable">
<thead>
<tr>
<th scope="col">Video Title</th>
<th scope="col">Related Lessons</th>
</tr>
</thead>
<tbody>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/v/adding-and-subtracting-polynomials-1?modal=1" target="_blank">Adding Polynomials</a></td>
<td><ul>
<li>Add and Subtract Polynomials</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:poly-add-sub/v/subtracting-polynomials?modal=1" target="_blank"> Subtracting Polynomials</a></td>
<td><ul>
<li>Add and Subtract Polynomials</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/v/multiply-monomials-intro?modal=1" target="_blank"> Multiplying Monomials</a></td>
<td><ul>
<li>Multiplying Polynomials</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-arithmetic/x2ec2f6f830c9fb89:mono-by-poly/v/multiplying-monomials-by-polynomials?modal=1" target="_blank">Multiplying Monomials by Polynomials</a></td>
<td><ul>
<li>Multiplying Polynomials</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:multiply-binomial/v/multiplying-binomials" target="_blank"> Multiplying Binomials</a></td>
<td><ul>
<li>Multiplying Polynomials</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-long-division-of-polynomials/v/dividing-polynomials-1" target="_blank">Dividing Polynomials: Long Division</a></td>
<td><ul>
<li>Dividing Polynomials</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor/x2ec2f6f830c9fb89:common-factor/v/factoring-and-the-distributive-property-3" target="_blank"> Taking a Common Factor from a Trinomial</a></td>
<td><ul>
<li>Greatest Common Factor and Factor by Grouping</li>
<li>Factor Trinomials</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-grouping/v/factoring-trinomials-by-grouping-5" target="_blank"> Factoring Quadratics: Common Factor + Grouping</a></td>
<td><ul>
<li>Greatest Common Factor and Factor by Grouping</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-quadratics-intro/v/factoring-simple-quadratic-expression" target="_blank">Factoring Quadratics as (x+a)(x+b)</a></td>
<td><ul>
<li>Factor Trinomials </li>
<li>General Strategy for Factoring Polynomials </li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-perfect-squares/v/factoring-perfect-square-trinomials" target="_blank">Factoring Perfect Squares</a></td>
<td><ul>
<li>Factor Special Products</li>
</ul></td>
</tr>
<tr>
<td><a href="https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:factor-difference-squares/v/difference-of-squares-intro" target="_blank">Difference of Squares Intro</a></td>
<td><ul>
<li>Factor Special Products</li>
</ul></td>
</tr>
</tbody>
</table>