{"id":123004,"date":"2022-05-30T11:26:07","date_gmt":"2022-05-30T16:26:07","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=123004"},"modified":"2026-03-28T11:52:57","modified_gmt":"2026-03-28T16:52:57","slug":"factoring-trinomials-of-the-form-x2bxc","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/factoring-trinomials-of-the-form-x2bxc\/","title":{"rendered":"Factoring Trinomials of the Form [latex]x^2+bx+c[\/latex]"},"content":{"rendered":"<h1>Factoring Trinomials of the Form \\(x^2+bx+c\\)<\/h1>\n\n\t\t\t<div id=\"mmDeferVideoEncompass_4B0hAUn1i_k\" 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_4B0hAUn1i_k\" data-source-videoID=\"4B0hAUn1i_k\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Factoring Trinomials of the Form [latex]x^2+bx+c[\/latex] Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Factoring Trinomials of the Form [latex]x^2+bx+c[\/latex]\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_4B0hAUn1i_k:hover {cursor:pointer;} img#videoThumbnailImage_4B0hAUn1i_k {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/2344-thumbnail-1-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_4B0hAUn1i_k\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_4B0hAUn1i_k\" 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 Trinomials of the Form [latex]x^2+bx+c[\/latex]\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_4B0hAUn1i_k\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_4B0hAUn1i_k\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_4B0hAUn1i_k\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello! Welcome to this video on factoring trinomials of the form \\(x^{2}+bx+c\\). An example of a trinomial like this is \\(x^{2}+8x+15\\). Let\u2019s go ahead and factor this <a href=\"https:\/\/www.mometrix.com\/academy\/factoring-polynomials\/\"><strong>trinomial<\/strong><\/a>. When we factor a trinomial, we want to break the trinomial into two expressions that, when multiplied together, gives you the original trinomial. Each of these expressions is a factor of the original trinomial, and they can help you find solutions to equations.<\/p>\n<p>When we factor a trinomial, we are going to use a process that is the reverse of the <a href=\"https:\/\/www.mometrix.com\/academy\/multiplying-terms-using-the-foil-method\/\"><strong>FOIL<\/strong><\/a> method. We start by writing two sets of parentheses.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((     )(     )\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now, we consider the first term, \\(x^{2}\\). What two things multiply together to get \\(x^{2}\\)? \\(x\\cdot x=x^{2}\\), so \\(x\\) will be the first term in both sets of parentheses.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((x    )(x    )\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Then, we need to find two numbers that multiply to the third term, 15, and add to the coefficient of the second term, 8. \\(3\\cdot 5=15\\) and \\(3+5=8\\), so our two numbers will be 3 and 5. Write \\(+3\\) in one set of parentheses after the \\(x\\) and \\(+5\\) in the other set of parentheses.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((x+3)(x+5)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Remember, factoring a trinomial is like \u201cun-FOILing\u201d it, so if we apply the FOIL method to this new expression, we should get our original trinomial. Let\u2019s do that now to check our work.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\(x^{2}+5x+3x+15\\)<br \/>\n&nbsp;<br \/>\n\\(x^{2}+8x+15\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Sure enough, we got our original trinomial, which means our factored form of \\((x+3)(x+5)\\) is correct!<\/p>\n<p>Let\u2019s try another one. Factor the trinomial \\(x^{2}+2x-63\\).<\/p>\n<p>First, set up two sets of parentheses.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((     )(     )\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Then, determine what two things multiply to \\(x^{2}\\). If the coefficient of \\(x^{2}\\) is 1, like all the examples in this video, it will always be \\(x\\cdot x\\), so let\u2019s go ahead and write an \\(x\\) in each set of parentheses.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((x    )(x    )\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Now, we need to find two numbers that multiply to \\(\u201363\\) and add to 2. Let\u2019s consider the factors of 63. We have 1 and 63, 3 and 21, and 7 and 9. Now, since our product is negative, we know that one of the factors will be positive and one will be negative. So we need to consider which two factors (remember, one being negative and one being positive) will add to 2. The two factors must be \\(\u20137\\) and 9. Write \\(-7\\) in one set of parentheses and \\(+9\\) in the other.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((x-7)(x+9)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>If we FOIL this out, we will get \\(x^{2}+2x-63\\), which is our original trinomial, so our factorization is correct.<\/p>\n<p>Before we go, let\u2019s work through one more example. Factor the trinomial \\(x^{2}-13x+22\\).<\/p>\n<p>First, set up the parentheses.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((     )(     )\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Then, put the \\(x\\)\u2019s where they belong, since \\(x\\cdot x=x^{2}\\).<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((x    )(x    )\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>Finally, we need to find two numbers that multiply to 22 and add to \\(\u201313\\). Since the two numbers add to a negative number but multiply to a positive number, both numbers have to be negative. <\/p>\n<p>Let\u2019s consider the factors of 22. We have \\(1\\times 22\\), and \\(2\\times 11\\). Which set of factors, when both numbers are negative, add to \\(\u201313\\)? The only option is \\(\u20132\\) and \\(\u201311\\), so we need to write \\(-2\\) in one set of parentheses and \\(-11\\) in the other set.<\/p>\n<blockquote style=\"border: 0px; padding: 30px; background-color: #eee; box-shadow: 1.5px 1.5px 5px grey; width:80%; margin: auto;\">\n<div style=\"font-style:normal; font-size:90%; text-align:center;\">\\((x-2)(x-11)\\)<\/div>\n<\/blockquote>\n<p>\n&nbsp;<\/p>\n<p>We can FOIL this out and get \\(x^{2}-13x+22\\), so that means our factored form, \\((x-2)(x-11)\\) is correct.<\/p>\n<p>Now there is one thing to note before we go. In the examples in this video, our trinomials factored out nicely. This isn&#8217;t possible for every single trinomial. And when you come across things like that, there are other options like <a href=\"https:\/\/www.mometrix.com\/academy\/completing-the-square\/\"><strong>completing the square<\/strong><\/a> or using the <a href=\"https:\/\/www.mometrix.com\/academy\/using-the-quadratic-formula\/\"><strong>quadratic formula<\/strong><\/a> to solve. However, when you are asked to factor trinomials of this form, you&#8217;ll know how to do it.<\/p>\n<p>I hope that this video on factoring trinomials of the form x2+bx+c was helpful. Thanks for watching, and happy studying!<\/p>\n<\/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>Factoring Trinomials of the Form Return to Algebra I Videos<\/p>\n","protected":false},"author":22,"featured_media":123013,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-123004","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/123004","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\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=123004"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/123004\/revisions"}],"predecessor-version":[{"id":290921,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/123004\/revisions\/290921"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/123013"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=123004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}