{"id":678,"date":"2013-05-28T14:29:09","date_gmt":"2013-05-28T14:29:09","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=678"},"modified":"2026-03-25T12:48:34","modified_gmt":"2026-03-25T17:48:34","slug":"factoring-quadratic-equations","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/factoring-quadratic-equations\/","title":{"rendered":"Factoring Quadratic Equations"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_UANzjP8_6qk\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_UANzjP8_6qk\" data-source-videoID=\"UANzjP8_6qk\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Factoring Quadratic Equations Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Factoring Quadratic Equations\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_UANzjP8_6qk:hover {cursor:pointer;} img#videoThumbnailImage_UANzjP8_6qk {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/259-solving-quadratic-equations-1-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_UANzjP8_6qk\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_UANzjP8_6qk\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Factoring Quadratic Equations\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_UANzjP8_6qk\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_UANzjP8_6qk\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_UANzjP8_6qk\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction GCk_Function() {\n  var x = document.getElementById(\"GCk\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"GCk_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"GCk\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_a_Quadratic_Equation\" class=\"smooth-scroll\">What is a Quadratic Equation?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Factoring_a_Quadratic_Equation\" class=\"smooth-scroll\">Factoring a Quadratic Equation<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Factoring_Quadratic_Equations_Practice_Questions\" class=\"smooth-scroll\">Factoring Quadratic Equations Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hey guys! Welcome to this video on factoring quadratic equations.<\/p>\n<h2><span id=\"What_is_a_Quadratic_Equation\" class=\"m-toc-anchor\"><\/span>What is a Quadratic Equation?<\/h2>\n<p>\nTo start, let\u2019s review what a quadratic equation actually is. The term <em>quadratic<\/em> is derived from <em>quad<\/em>, which means &#8220;square,&#8221; and we call it this because the variable is squared.<\/p>\n<p>Now, the standard form of a quadratic equation is this:<\/p>\n<div class=\"examplesentence\">\\(ax^2 +bx + c = 0\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Factoring_a_Quadratic_Equation\" class=\"m-toc-anchor\"><\/span>Factoring a Quadratic Equation<\/h2>\n<p>\nIn order to factor a quadratic, you just need to find what you would multiply by in order to get the quadratic. The actual quadratic equation is the expanded, or multiplied out version, of your two <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/factors\/\">factors<\/a> that are being multiplied.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nFor example, \\((x + 2)\\) and \\((x + 6)\\) are my factors that are being multiplied together. Once you multiply together you get \\(x^2+ 8x + 12\\).<\/p>\n<p>So, again we have our factors \\((x + 2)(x + 6)\\) on the left, and when you multiply that you get the expanded version: \\((x^2+ 8x + 12)\\).<\/p>\n<p>Now, expanding can be pretty easy; we know exactly what to do to expand them when given our factors, but figuring out how to factor our expanded version can be a little harder.<\/p>\n<p>The easiest way to do this is to find the <strong>common factor<\/strong>.<\/p>\n<p>Let\u2019s look at how to do that. Say we have the equation \\(8x^2 + 16x = 0\\)<\/p>\n<p>What are the common factors of \\(8x^2 + 16x = 0\\)?<\/p>\n<p>Well, 8 and 16 share a common factor of 8. So, we can go ahead and factor out that 8.<\/p>\n<p>Now, we have \\(8(x^2 + 2x)\\) being multiplied by everything on the inside. But, we still have something that can be factored out. \\(x^2\\) and \\(x\\) share a common factor of \\(x\\). So, now we have \\(8x(x + 2)\\). And we\u2019ve got it. Our factors of the equation \\(8x^2 + 16x = 0\\) are \\(8x\\) and \\(x + 2\\).<\/p>\n<p>Maybe you\u2019re asking, why on earth do I even need to factor? Why can\u2019t I just leave it as it is?<\/p>\n<p>Well, if you recall a quadratic equation is always a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/parabolas\/\">parabola<\/a> (or U-shaped graph). Well, factoring the quadratic equation then sets us up to be able to find out where exactly our roots are, and our roots just mean where our graph is equal to zero.<\/p>\n<p>To do that, we would set our factors equal to zero and solve.<\/p>\n<p>So, \\(8x\\) is \\(0\\) when \\(x = 0\\), and \\(x + 2\\) is \\(0\\) when \\(x = -2\\).<\/p>\n<p>When we look at the graph for \\(8x^2+ 16x = 0\\), we can see that it\u2019s zero at \\(x = 0\\) and \\(x = -2\\).<\/p>\n<p>All right, so that is kind of a side note to answer the question \u201cwhy does factoring matter?\u201d<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nBut now, let\u2019s look back at how to actually factor. In our last example, it was relatively simple to find a common factor for the two numbers 8 and 16. However, our numbers aren\u2019t always so straightforward. So, it may be we don\u2019t just know the factors off the top of our head, and guessing might not be as quick as we would hope. So, then what would we do?<\/p>\n<p>Well, let\u2019s look at an example of one of these equations that may be a little trickier to factor.<\/p>\n<div class=\"examplesentence\">\\(2x^2+ x &#8211; 6\\)<\/div>\n<p>\n&nbsp;<br \/>\nOkay, so I don\u2019t know about you, but I am not at the point where I can just look at this equation and just know off the top of my head what the factors are. So, I have to follow a kind of step-by-step method that works when we have a quadratic equation in standard form.<\/p>\n<p>So, here are the steps that you should follow:<\/p>\n<ol>\n<li style=\"margin-bottom:10px;\">Identify which two numbers will multiply to get \\(a\\times c\\), and add together to get \\(b\\).<\/li>\n<li style=\"margin-bottom:10px;\">Replace the middle of the equation with the two factors that you found<\/li>\n<li style=\"margin-bottom:10px;\">Group together the first two terms and the last two terms, then factor them individually<\/li>\n<li>The two terms, at this point, should now have an obvious common factor<\/li>\n<\/ol>\n<p>Let\u2019s look at how to factor the equation \\(2x^2 + x &#8211; 6\\) using these four steps.<\/p>\n<h4 style=\"margin-bottom: 0.25em;\"><span id=\"Step_1\" class=\"m-toc-anchor\"><\/span>Step 1<\/h4>\n<p>\nSo, first, we need to identify which two numbers multiply together to get \\(a\\times c\\), which is -12, and add to get \\(b\\) (positive 1). So, let\u2019s go ahead and list all the possible factors of 12. So, obviously there is 1 and 12, then 2 and 6, and lastly 3 and 4. Remember, we are actually dealing with a -12, so we need to consider that when choosing which two factors work. So, we need these factors to multiply to get -12, which each of them will if we through a negative sign in front of one of the factors, but we also need for it to add to get positive one. So, the only way that can happen is if we take the two factors 3 and 4, and throw a negative sign in front of 3. That makes our factors -3 and 4, which multiplies to give us -12 and add to give us positive 1. So, on to step 2.<\/p>\n<h4 style=\"margin-bottom: 0.25em;\"><span id=\"Step_2\" class=\"m-toc-anchor\"><\/span>Step 2<\/h4>\n<p>\nStep two tells us to replace the middle of the equation with the two factors that we found. Doing that gives us \\(2x^2 -3x + 4x -6\\). <\/p>\n<h4 style=\"margin-bottom: 0.25em;\"><span id=\"Step_3\" class=\"m-toc-anchor\"><\/span>Step 3 <\/h4>\n<p>\nStep 3 tells us to group together the first two terms, and the last two terms, then factor them individually. So, we would group together \\((2x^2 &#8211; 3x) + (4x-6)\\), then factor. From the first two terms, we can factor out an \\(x\\), which would give us \\(x(2x &#8211; 3)\\). From the last two terms, we can factor out a 2, which would give us \\(2(2x &#8211; 3)\\). So, now we have \\(x(2x &#8211; 3) + 2(2x &#8211; 3)\\).<\/p>\n<h4 style=\"margin-bottom: 0.25em;\"><span id=\"Step_4\" class=\"m-toc-anchor\"><\/span>Step 4<\/h4>\n<p>\nNow, lastly, step number four tells us that we should be able to see an obvious common factor, which we have. \\((2x &#8211; 3)\\) is common to both terms, so we can write this as \\((x + 2)(2x &#8211; 3)\\), and we have our answer. To check this, we can multiply this out to see if you get our original expanded quadratic equation.<\/p>\n<p>So, when we expand we get \\(2x^2-3x + 4x &#8211; 6\\), and when we simplify that we get \\(2x^2+ x &#8211; 6\\), which is our original equation. Great work, guys!<\/p>\n<p>I hope that this video on how to factor quadratic equations was helpful. <\/p>\n<p>See you guys next time!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Factoring_Quadratic_Equations_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Factoring Quadratic Equations Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFactor the quadratic equation:<\/p>\n<div class=\"yellow-math-quote\">\\(x^2+5x+6\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\((x+6)(x+7)\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\((x+2)(x+9)\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">\\((x+2)(x+3)\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\((x+8)(x+4)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The quadratic equation is currently in expanded form, with \\(a=1\\), \\(b=5\\), and \\(c=6\\).<\/p>\n<p>First, find two numbers that multiply to \\(a \\times c\\) and add to get \\(b\\). In this case, the two numbers need to multiply to 6 and add to 5. The only two numbers that can do this are 2 and 3.<\/p>\n<p>Then, replace the middle of the equation with these two factors to get \\(x^2+2x+3x+6\\). Group the first two terms and last two terms and factor them individually.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\((x^2+2)+(3x+6)\\)<br \/>\n\\(x(x+2)+3(x+2)\\)\n<\/p>\n<p>Now, look for the common factor that they both share. In this case, it\u2019s \\((x+2)\\) and \\((x+3)\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFactor the quadratic equation:<\/p>\n<div class=\"yellow-math-quote\">\\(x^2-2x-35\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\((x+3)(x-2)\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">\\((x-7)(x+5)\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\((x+4)(x+9)\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\((x-3)(x-6)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The quadratic equation is currently in expanded form, with \\(a=1\\), \\(b=-2\\), and \\(c=-35\\).<\/p>\n<p>First, find two numbers that multiply to \\(a \\times c\\) and add to get \\(b\\). In this case, the two numbers need to multiply to \u221235 and add to \u22122. The only two numbers that can do this are \u22127 and 5.<\/p>\n<p>Then, replace the middle of the equation with these two factors to get \\(x^2-7x+5x-35\\). Group the first two terms and last two terms and factor them individually.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\((x^2-7x)+(5x-35)\\)<br \/>\n\\(x(x-7)+5(x-7)\\)\n<\/p>\n<p>Now, look for the common factor that they both share. In this case, it\u2019s \\((x-7)\\) and \\((x+5)\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFactor the quadratic equation:<\/p>\n<div class=\"yellow-math-quote\">\\(x^2-2x-15\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\">\\((x-5)(x+3)\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\((x-6)(x-4)\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\((x-5)(x+4)\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\((x-6)(x-2)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The quadratic equation is currently in expanded form, with \\(a=1\\), \\(b=-2\\), and \\(c=-15\\).<\/p>\n<p>First, find two numbers that multiply to \\(a \\times c\\) and add to get \\(b\\). In this case, the two numbers need to multiply to \u221215 and add to \u22122. The only two numbers that can do this are \u22125 and 3. These two factors multiply to the original equation that is in expanded form, so the equation has been successfully factored.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFactor the quadratic equation:<\/p>\n<div class=\"yellow-math-quote\">\\(3x^2-2x-5\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\((x+2)(x-5)\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\((4x+4)(5x-1)\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">\\((3x-5)(x+1)\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\((3x+2)(x-5)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The quadratic equation is currently in expanded form, with \\(a=3\\), \\(b=-2\\), and \\(c=-5\\).<\/p>\n<p>First, find two numbers that multiply to \\(a \\times c\\) and add to get \\(b\\). In this case, the two numbers need to multiply to \u221215 and add to \u22122. The only two numbers that can do this are \u22125 and 3.<\/p>\n<p>Then, replace the middle of the equation with these two factors to get \\(3x^2-5x+3x-5\\). Group the first two terms and last two terms and factor them individually.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\((3x^2-5x)+(3x-5)\\)<br \/>\n\\(x(3x-5)+1(3x-5)\\)\n<\/p>\n<p>Now, look for the common factor that they both share. In this case, it\u2019s \\((3x-5)\\) and \\((x+1)\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nFactor the quadratic equation:<\/p>\n<div class=\"yellow-math-quote\">\\(3x^2-x-4\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\((6x-3)(x+1)\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">\\((3x-4)(x+1)\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\((2x-1)(x+8)\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\((x+4)(x-1)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The quadratic equation is currently in expanded form, with \\(a=3\\), \\(b=-1\\), and \\(c=-4\\).<\/p>\n<p>First, find two numbers that multiply to \\(a \\times c\\) and add to get \\(b\\). In this case, the two numbers need to multiply to \u221212 and add to \u22121. The only two numbers that can do this are \u22124 and 3.<\/p>\n<p>Then, replace the middle of the equation with these two factors to get \\(3x^2-4x+3x-4\\). Group the first two terms and last two terms and factor them individually.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\((3x^2-4x)+(3x-4)\\)<br \/>\n\\(x(3x-4)+1(3x-4)\\)\n<\/p>\n<p>Now, look for the common factor that they both share. In this case, it\u2019s \\((3x-4)\\) and \\((x+1)\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":1,"featured_media":91387,"parent":0,"menu_order":31,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-678","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-quadratics-videos","8":"page_type-video","9":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/678","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=678"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/678\/revisions"}],"predecessor-version":[{"id":279433,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/678\/revisions\/279433"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/91387"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}