{"id":194,"date":"2022-04-13T10:18:02","date_gmt":"2022-04-13T10:18:02","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=194"},"modified":"2024-08-25T07:58:14","modified_gmt":"2024-08-25T07:58:14","slug":"j-5-solve-a-quadratic-equation-by-factorising","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-5-solve-a-quadratic-equation-by-factorising\/","title":{"rendered":"J.5 Solve a quadratic equation by factorising"},"content":{"rendered":"\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Solve a quadratic equation by factorising<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-b3b52819700451632df7398176ff5306\" style=\"color:#b8e612\"><strong>Understanding Factoring<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factoring is the process of breaking down a polynomial expression into simpler expressions (factors) that can be multiplied together to obtain the original expression.<\/li>\n\n\n\n<li>In the context of quadratic equations, factoring involves finding two binomial expressions that multiply together to give the original equation.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-e5ea717fb748f3be316a95cdc432d47d\" style=\"color:#5bed07\"><strong>Steps to Solve by Factoring<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Express the Quadratic Equation in Standard Form:<\/strong> Ensure the equation is in the form ax\u00b2 + bx + c = 0.<\/li>\n\n\n\n<li><strong>Factor the Quadratic Expression:<\/strong> Find two binomial expressions that multiply together to give the original quadratic expression. This often involves finding two numbers that add up to b and multiply to c.<\/li>\n\n\n\n<li><strong>Set Each Factor Equal to Zero:<\/strong> Once the equation is factored, set each factor equal to zero.<\/li>\n\n\n\n<li><strong>Solve for x:<\/strong> Solve each resulting equation to find the values of x that make the factors zero.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-8ba3d4db2b70a02d08f615db1c02d63e\" style=\"color:#dc1e1e\"><strong>Example<\/strong><\/p>\n\n\n\n<p>Solve: x\u00b2 &#8211; 5x + 6 = 0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: The equation is already in standard form.<\/li>\n\n\n\n<li>Step 2: Factor the equation: (x &#8211; 2)(x &#8211; 3) = 0<\/li>\n\n\n\n<li>Step 3: Set each factor equal to zero:\n<ul class=\"wp-block-list\">\n<li>x &#8211; 2 = 0<\/li>\n\n\n\n<li>x &#8211; 3 = 0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Step 4: Solve each equation:\n<ul class=\"wp-block-list\">\n<li>x = 2<\/li>\n\n\n\n<li>x = 3<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-9bb12b1a052aa54d07ccb542307efd6f\" style=\"color:#1b45da\"><strong>Key Points<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factoring is a powerful technique for solving quadratic equations.<\/li>\n\n\n\n<li>The goal is to find two binomial expressions that multiply to give the original equation.<\/li>\n\n\n\n<li>Once factored, set each factor equal to zero and solve for x.<\/li>\n\n\n\n<li>Not all quadratic equations can be factored easily. In such cases, other methods like completing the square or the quadratic formula can be used.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#eaa9fd\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Solve&nbsp;for&nbsp;w.<\/strong><\/p>\n\n\n\n<p>w<sup>2<\/sup>+19w\u201320=0<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5e55411f864f26ea906397d84fb813d8\" style=\"color:#b00012\"><strong>Write&nbsp;each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with&nbsp;commas.<\/strong><\/p>\n\n\n\n<p>w=________<\/p>\n<\/div><\/div>\n\n\n\n<p><strong>Step&nbsp;1:&nbsp;Factor.<\/strong><\/p>\n\n\n\n<p>The&nbsp;c&nbsp;term is&nbsp;\u201320,&nbsp;so you need to find a pair of factors with a product of&nbsp;\u201320.&nbsp;The&nbsp;b&nbsp;term is&nbsp;19,&nbsp;so you need to find a pair of factors with a sum of&nbsp;19.&nbsp;Since the product is negative&nbsp;(\u201320),&nbsp;you need one factor to be negative and one factor to be&nbsp;positive.<\/p>\n\n\n\n<p>Make&nbsp;a list of the possible factor pairs with a product of&nbsp;\u201320,&nbsp;and then find the one with a sum of&nbsp;19.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">Factor Pairs of c = -20<\/td><td class=\"has-text-align-center\" data-align=\"center\">Sum of factor pairs <\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1 . -20 = -20<\/td><td class=\"has-text-align-center\" data-align=\"center\">1 + -20 = &#8211; 19<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1 . 20 = -20<\/td><td class=\"has-text-align-center\" data-align=\"center\">-1 + 20 = 19<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2 . 10 = -20<\/td><td class=\"has-text-align-center\" data-align=\"center\">2 + &#8211; 10 = -8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2 .10 = -20<\/td><td class=\"has-text-align-center\" data-align=\"center\">-2 + 10 =  8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">4 . -5 = -20<\/td><td class=\"has-text-align-center\" data-align=\"center\">4 + -5 = -1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">&#8211; 4 .5 = -20<\/td><td class=\"has-text-align-center\" data-align=\"center\">-4 + 5 = 1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The&nbsp;factors&nbsp;20&nbsp;and&nbsp;\u20131&nbsp;have a sum of&nbsp;19.&nbsp;Use those numbers to factorise&nbsp;w2+19w\u201320.<\/p>\n\n\n\n<p>w2+19w\u201320=0<\/p>\n\n\n\n<p>(w+<strong>20<\/strong>)(w\u2013<strong>1<\/strong>)=0<\/p>\n\n\n\n<p><strong>Step&nbsp;2: Use the zero product property to&nbsp;solve.<\/strong><\/p>\n\n\n\n<p>According&nbsp;to the zero product property, if&nbsp;(w+20)(w\u20131)=0,&nbsp;then&nbsp;w+20&nbsp;must be 0 or&nbsp;w\u20131&nbsp;must be 0. Write the two equations and solve for&nbsp;w.<\/p>\n\n\n\n<p>w+20=0          or            w\u20131=0<\/p>\n\n\n\n<p>      w=-20                                    w<strong>=1<\/strong><\/p>\n\n\n\n<p>The&nbsp;solutions are&nbsp;w=\u201320&nbsp;and&nbsp;w=1.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c1f398\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Solve&nbsp;for&nbsp;q.<\/strong><\/p>\n\n\n\n<p>q<sup>2<\/sup>\u201325q=0<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5e55411f864f26ea906397d84fb813d8\" style=\"color:#b00012\"><strong>Write&nbsp;each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with&nbsp;commas.<\/strong><\/p>\n\n\n\n<p>q=________<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p><strong>Step&nbsp;1:&nbsp;Factor.<\/strong><\/p>\n\n\n\n<p>q<sup>2<\/sup>\u201325q=0<\/p>\n\n\n\n<p>q(q\u201325)=0     Factor&nbsp;out the highest common factor,&nbsp;q<\/p>\n\n\n\n<p><strong>Step&nbsp;2: Use the zero product property to&nbsp;solve.<\/strong><\/p>\n\n\n\n<p>According&nbsp;to the zero product property, if&nbsp;q(q\u201325)=0,&nbsp;then&nbsp;q&nbsp;must be 0 or&nbsp;q\u201325&nbsp;must be 0. Write the two equations and solve for&nbsp;q.<\/p>\n\n\n\n<p>q<strong>=0<\/strong>          or       q\u201325=0<\/p>\n\n\n\n<p>                              q<strong>=25<\/strong><\/p>\n\n\n\n<p>The&nbsp;solutions are&nbsp;q=0&nbsp;and&nbsp;q=25.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f8cda4\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Solve&nbsp;for&nbsp;d.<\/strong><\/p>\n\n\n\n<p>d<sup>2<\/sup>+33d=0<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-5e55411f864f26ea906397d84fb813d8\" style=\"color:#b00012\"><strong>Write&nbsp;each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with&nbsp;commas.<\/strong><\/p>\n\n\n\n<p>d=________<\/p>\n<\/div><\/div>\n\n\n\n<p><strong>Step&nbsp;1:&nbsp;Factor.<\/strong><\/p>\n\n\n\n<p>d<sup>2<\/sup>+33d=0<\/p>\n\n\n\n<p>d(d+33)=0     Factor&nbsp;out the highest common factor,&nbsp;d<\/p>\n\n\n\n<p><strong>Step&nbsp;2: Use the zero product property to&nbsp;solve.<\/strong><\/p>\n\n\n\n<p>According&nbsp;to the zero product property, if&nbsp;d(d+33)=0,&nbsp;then&nbsp;d&nbsp;must be 0 or&nbsp;d+33&nbsp;must be 0. Write the two equations and solve for&nbsp;d.<\/p>\n\n\n\n<p>d<strong>=0<\/strong>        or      d+33=0<\/p>\n\n\n\n<p>                         d<strong>=<\/strong>\u2013<strong>33<\/strong><\/p>\n\n\n\n<p>The&nbsp;solutions are&nbsp;d=0&nbsp;and&nbsp;d=\u201333.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76703\/974\/772\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-52.png\" alt=\"\" class=\"wp-image-6945\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-52.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-52-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-52-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76716\/894\/163\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-70.png\" alt=\"\" class=\"wp-image-6946\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-70.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-70-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-70-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve a quadratic equation by factorising Key Notes : Understanding Factoring Steps to Solve by Factoring Example Solve: x\u00b2 &#8211; 5x + 6 = 0 Key Points Learn with an example Solve&nbsp;for&nbsp;w. w2+19w\u201320=0 Write&nbsp;each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with&nbsp;commas. w=________<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-5-solve-a-quadratic-equation-by-factorising\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.5 Solve a quadratic equation by factorising&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-194","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/194","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=194"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/194\/revisions"}],"predecessor-version":[{"id":13680,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/194\/revisions\/13680"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}