{"id":5690,"date":"2022-02-06T12:14:40","date_gmt":"2022-02-06T12:14:40","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5690"},"modified":"2022-02-06T12:16:45","modified_gmt":"2022-02-06T12:16:45","slug":"factoring-algebraic-expressions-word-problems","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/factoring-algebraic-expressions-word-problems\/","title":{"rendered":"Factoring Algebraic Expressions Word Problems"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Factoring Algebraic Expressions Word Problems<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Factorization of algebraic means finding the factors of the given expression which refers to finding two or more expressions whose product is the given expression. This process of finding two or more expressions whose product is the given expression is known as the factorization of algebraic expressions. A factor is a number that divides the given number without any remainder. It simply means expressing a number as a multiplication of two other numbers. Similarly, in Algebra we write the algebraic expressions as a product of their factors. The only difference here is that an algebraic expression involves numbers and variables combined with an arithmetic operation like addition or subtraction.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Read the word problem and determine the greatest common factor of the terms.<br \/>\n2. Keep the greatest common factor outside the brackets, divide the polynomial terms by this factor and write the remaining expression inside the brackets.<br \/>\n3. Verify your answer by multiplying the factors to get the original expression.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<span style=\"color: #16a085;\"><strong>A rectangular garden is being separated into 6 equal sections for different types of flowers. The area of the garden is (12x + 30) square meters. What is the area of each section of the garden?<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]1. Find the greatest common factor of the two terms.<br \/>\nThe greatest common factor of 12 and 30 is 6.<\/p>\n<p>2. Keep the greatest common factor outside the brackets, divide the polynomial terms by this factor and write the remaining expression inside the brackets.<br \/>\n(12x + 30) = (6 \u25cf 2x) + (6 \u25cf 5)<br \/>\n6(2x + 5)<\/p>\n<p>3. Verify your answer by multiplying the factors to get the original expression.<br \/>\n6(2x + 5)<br \/>\n12x + 30<\/p>\n<p>Therefore, the area of each section of the garden is <strong><span style=\"color: #ff0000;\">(2x + 5)<\/span><\/strong> square meters.<br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Factoring Algebraic Expressions Word Problems[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Ralph spends 14z + 21 dollars every week. How much money does he spend daily?<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions\"><img loading=\"lazy\" class=\"alignnone wp-image-5368 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/1-23.png\" alt=\"\" width=\"105\" height=\"43\" \/><\/a><br \/>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Each friend has (<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{\\color{Teal}&space;\\frac{x}{4}}\" alt=\"\\fn_phv {\\color{Teal} \\frac{x}{4}}\" align=\"absmiddle\" \/> + 3) apples, and there are 4 friends. How many apples are there altogether?<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions\"><img loading=\"lazy\" class=\"alignnone wp-image-5692 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/57.png\" alt=\"\" width=\"158\" height=\"46\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Sam shared his marbles with seven friends. Each friend has (7n – 1) marbles. How many marbles did Sam start with?<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions\"><img loading=\"lazy\" class=\"alignnone wp-image-5694 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/58.png\" alt=\"\" width=\"161\" height=\"45\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/factor-linear-expressions”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Factor<\/strong> – is a number that divides the given number without any remainder.<\/p>\n<p><strong>Linear Expression<\/strong> \u2013 an algebraic expression in which the variable is raised to the first power, and variables are not multiplied or divided.<\/p>\n<p><strong>Term<\/strong> \u2013 either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or \u2212 signs.<\/p>\n<p><strong>Like terms<\/strong> – Terms that have the same power for the same variables. In like terms, one can only change the numerical coefficient.<\/p>\n<p><strong>Unlike terms<\/strong> – Terms that have different variables or the same variables raised to different powers.<\/p>\n<p><strong>Distributive Property<\/strong> \u2013 to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis.<\/p>\n<p><strong>Constant<\/strong> \u2013 a term without a variable.<\/p>\n<p><strong>Variable<\/strong> – In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation or expression.<\/p>\n<p><strong>Coefficient<\/strong> – is an integer that is multiplied with the variable of a single term or the terms of a polynomial.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1637574855789{border-radius: 10px !important;}”]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/identify-factors\"><span style=\"color: #ed5600;\">Identify Factors<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/greatest-common-factor-gcf\"><span style=\"color: #ed5600;\">Greatest Common Factor-GCF<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/arithmetic-sequences\"><span style=\"color: #ed5600;\">Arithmetic Sequences<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/geometric-sequences\"><span style=\"color: #ed5600;\">Geometric Sequences<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/the-distributive-property\"><span style=\"color: #ed5600;\">The Distributive Property<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/simplifying-complex-algebraic-expressions\"><span style=\"color: #ed5600;\">Simplifying Complex Algebraic Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/add-linear-expressions\"><span style=\"color: #ed5600;\">Add Linear Expressions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/subtract-linear-expressions\"><span style=\"color: #ed5600;\">Subtract Linear Expressions<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1637575211592{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 10px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-addition-and-subtraction\">Solve One-Step Equations by Addition and Subtraction<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-one-step-equations-by-multiplying-and-dividing\">Solve One-Step Equations by Multiplying and Dividing<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-equations-with-rational-coefficients\">Solve Equations with Rational Coefficients<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-two-step-equations\">Solve Two-Step Equations<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solve-complex-equations\">Solve Complex Equations<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-equations-with-rational-coefficients\">Solve Equations with Rational Coefficients<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-two-step-equations\">Solve Two-Step Equations<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-two-step-equations\">Write Two-Step Equations<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/Solve%20Two-Sided%20Equations%20with%20Rational%20Coefficients\">Solve Two-Sided Equations with Rational Coefficients<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations\">Solve Multi-Step Equations<\/a><\/span>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” 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width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Factoring Algebraic Expressions Word Problems [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Factorization of algebraic means finding the factors of the given expression which refers to finding two or more expressions whose product is the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Factoring Algebraic Expressions Word Problems | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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