{"id":8694,"date":"2026-01-19T23:19:06","date_gmt":"2026-01-20T04:19:06","guid":{"rendered":"https:\/\/www.ezcalculatoronline.com\/?page_id=8694"},"modified":"2026-05-12T23:18:48","modified_gmt":"2026-05-13T04:18:48","slug":"factoring-trinomials","status":"publish","type":"page","link":"https:\/\/www.ezcalculatoronline.com\/math\/factoring-trinomials\/","title":{"rendered":"Factoring Trinomials"},"content":{"rendered":"<div id=\"tdi_1\" class=\"tdc-zone\"><div class=\"tdc_zone tdi_2  wpb_row td-pb-row\"  >\n<style scoped>\n\n\/* custom css *\/\n.tdi_2{\r\n                    min-height: 0;\r\n                }\n<\/style><div id=\"tdi_3\" class=\"tdc-row\"><div class=\"vc_row tdi_4  wpb_row td-pb-row\" >\n<style scoped>\n\n\/* custom css *\/\n.tdi_4,\r\n                .tdi_4 .tdc-columns{\r\n                    min-height: 0;\r\n                }.tdi_4,\r\n\t\t\t\t.tdi_4 .tdc-columns{\r\n\t\t\t\t    display: block;\r\n\t\t\t\t}.tdi_4 .tdc-columns{\r\n\t\t\t\t    width: 100%;\r\n\t\t\t\t}\n<\/style><div class=\"vc_column tdi_6  wpb_column vc_column_container tdc-column td-pb-span8\">\n<style scoped>\n\n\/* custom css *\/\n.tdi_6{\r\n                    vertical-align: baseline;\r\n                }.tdi_6 > .wpb_wrapper,\r\n\t\t\t\t.tdi_6 > .wpb_wrapper > .tdc-elements{\r\n\t\t\t\t    display: block;\r\n\t\t\t\t}.tdi_6 > .wpb_wrapper > .tdc-elements{\r\n\t\t\t\t    width: 100%;\r\n\t\t\t\t}.tdi_6 > .wpb_wrapper > .vc_row_inner{\r\n\t\t\t\t    width: auto;\r\n\t\t\t\t}.tdi_6 > .wpb_wrapper{\r\n\t\t\t\t    width: auto;\r\n\t\t\t\t    height: auto;\r\n\t\t\t\t}\n<\/style><div class=\"wpb_wrapper\" ><div class=\"wpb_wrapper td_block_wrap vc_raw_html tdi_8 \">\n<style scoped>\n\n\/* inline tdc_css att *\/\n\n.tdi_8{\nmargin-top:20px !important;\n}\n\n\/* phone *\/\n@media (max-width: 767px)\n{\n.tdi_8{\nmargin-top:20px !important;\n}\n}\n\n<\/style><div class=\"td-fix-index\"><!DOCTYPE html>\n<html lang=\"en\">\n<head>\n    <meta charset=\"UTF-8\">\n    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n    <title>Factoring Trinomials Calculator<\/title>\n    <style>\n        :root {\n            --primary: #4a90e2;\n            --secondary: #f5f7fa;\n            --text: #2c3e50;\n            --success: #27ae60;\n            --error: #e74c3c;\n            --border: #dce4ec;\n        }\n\n        body {\n            font-family: 'Segoe UI', Roboto, Helvetica, Arial, sans-serif;\n            background-color: #f0f2f5;\n            justify-content: center;\n            color: var(--text);\n        }\n\n        .container {\n            background: white;\n            width: 100%;\n            max-width: 700px;\n            border-radius: 12px;\n            box-shadow: 0 4px 20px rgba(0,0,0,0.08);\n            overflow: hidden;\n        }\n\n        .header {\n            background: var(--primary);\n            color: white;\n            padding: 20px;\n            text-align: center;\n        }\n\n        .header h1 { margin: 0; font-size: 1.5rem; }\n        .header p { margin: 5px 0 0; opacity: 0.9; font-size: 0.9rem; }\n\n        .input-section {\n            padding: 25px;\n            background: #fff;\n            border-bottom: 1px solid var(--border);\n            text-align: center;\n        }\n\n        .equation-input {\n            display: flex;\n            justify-content: center;\n            align-items: center;\n            gap: 10px;\n            font-size: 1.2rem;\n            margin-bottom: 20px;\n            font-weight: bold;\n        }\n\n        input {\n            width: 60px;\n            padding: 8px;\n            border: 2px solid var(--border);\n            border-radius: 8px;\n            text-align: center;\n            font-size: 1.1rem;\n            outline: none;\n            transition: 0.2s;\n        }\n\n        input:focus { border-color: var(--primary); }\n\n        .btn-solve {\n            background: var(--primary);\n            color: white;\n            border: none;\n            padding: 12px 30px;\n            border-radius: 25px;\n            font-size: 1rem;\n            font-weight: 600;\n            cursor: pointer;\n            transition: 0.2s;\n            box-shadow: 0 4px 6px rgba(74, 144, 226, 0.3);\n        }\n\n        .btn-solve:hover { transform: translateY(-2px); box-shadow: 0 6px 12px rgba(74, 144, 226, 0.4); }\n\n        #solution-area {\n            padding: 0;\n            display: none;\n            background: var(--secondary);\n        }\n\n        .step-card {\n            background: white;\n            margin: 20px;\n            padding: 20px;\n            border-radius: 10px;\n            border-left: 5px solid var(--primary);\n            box-shadow: 0 2px 5px rgba(0,0,0,0.05);\n        }\n\n        .step-title {\n            font-weight: bold;\n            color: var(--primary);\n            text-transform: uppercase;\n            font-size: 0.8rem;\n            letter-spacing: 1px;\n            margin-bottom: 10px;\n        }\n\n        .math-block {\n            font-family: 'Courier New', Courier, monospace;\n            background: #f8f9fa;\n            padding: 10px;\n            border-radius: 6px;\n            margin: 10px 0;\n            border: 1px dashed #cbd5e0;\n            font-weight: bold;\n        }\n\n        .explanation {\n            font-size: 0.95rem;\n            line-height: 1.5;\n            color: #555;\n        }\n\n        .final-answer {\n            background: var(--success);\n            color: white;\n            text-align: center;\n            padding: 20px;\n            font-size: 1.5rem;\n            font-weight: bold;\n        }\n\n        .fraction {\n            display: inline-block;\n            text-align: center;\n            vertical-align: middle;\n            margin: 0 2px;\n        }\n        .fraction > span { display: block; padding: 0 2px; }\n        .fraction span.bottom { border-top: 1px solid black; }\n        \n        \/* Highlight specific numbers *\/\n        .hl { color: var(--primary); font-weight: bold; }\n    <\/style>\n<\/head>\n<body>\n\n<div class=\"container\">\n    <div class=\"header\">\n        <h1>Factoring Trinomials Calculator\n<\/h1>\n        <p>Detailed steps for Students<\/p>\n    <\/div>\n\n    <div class=\"input-section\">\n        <div class=\"equation-input\">\n            <input type=\"number\" id=\"a\" value=\"2\"> x\u00b2 +\n            <input type=\"number\" id=\"b\" value=\"-5\"> x +\n            <input type=\"number\" id=\"c\" value=\"-3\">\n        <\/div>\n        <button class=\"btn-solve\" onclick=\"solve()\">Show Steps<\/button>\n    <\/div>\n\n    <div id=\"solution-area\"><\/div>\n<\/div>\n\n<script>\n    function getGCD(a, b) {\n        return b === 0 ? a : getGCD(b, a % b);\n    }\n\n    function solve() {\n        const aInput = document.getElementById('a').value;\n        const bInput = document.getElementById('b').value;\n        const cInput = document.getElementById('c').value;\n        const solutionArea = document.getElementById('solution-area');\n\n        if(aInput == '' || bInput == '' || cInput == '') {\n            alert(\"Please enter all coefficients!\");\n            return;\n        }\n\n        const a = parseInt(aInput);\n        const b = parseInt(bInput);\n        const c = parseInt(cInput);\n\n        if(a === 0) {\n            alert(\"Coefficient 'a' cannot be 0.\");\n            return;\n        }\n\n        let html = \"\";\n        \n        \/\/ --- Step 1: Identify ---\n        html += `\n        <div class=\"step-card\">\n            <div class=\"step-title\">Step 1: Identify Coefficients<\/div>\n            <div class=\"explanation\">\n                From the equation <span class=\"hl\">${a}x\u00b2 + ${b}x + ${c}<\/span>, we have:\n            <\/div>\n            <div class=\"math-block\">a = ${a}, b = ${b}, c = ${c}<\/div>\n        <\/div>`;\n\n        \/\/ --- Step 2: Discriminant ---\n        const delta = b*b - 4*a*c;\n        html += `\n        <div class=\"step-card\">\n            <div class=\"step-title\">Step 2: Calculate Discriminant (\u0394)<\/div>\n            <div class=\"explanation\">\n                Formula: \u0394 = b\u00b2 - 4ac\n            <\/div>\n            <div class=\"math-block\">\n                \u0394 = (${b})\u00b2 - 4(${a})(${c})<br>\n                \u0394 = ${b*b} - (${4*a*c})<br>\n                \u0394 = ${delta}\n            <\/div>\n        <\/div>`;\n\n        \/\/ --- Logic Branching ---\n        if (delta < 0) {\n            html += `\n            <div class=\"step-card\" style=\"border-left-color: var(--error);\">\n                <div class=\"step-title\" style=\"color: var(--error);\">Conclusion<\/div>\n                <div class=\"explanation\">\n                    Since \u0394 < 0, the equation has no real roots.\n                <\/div>\n                <div class=\"math-block\" style=\"color: var(--error);\">Cannot factor over real numbers.<\/div>\n            <\/div>`;\n        } else {\n            const sqrtDelta = Math.sqrt(delta);\n            \n            if (!Number.isInteger(sqrtDelta)) {\n                \/\/ Irrational\n                html += `\n                <div class=\"step-card\">\n                    <div class=\"step-title\">Step 3: Check Perfect Square<\/div>\n                    <div class=\"explanation\">\n                        \u0394 = ${delta} is not a perfect square. The roots are irrational numbers.\n                    <\/div>\n                    <div class=\"math-block\">Cannot factor into integers.<\/div>\n                <\/div>`;\n            } else {\n                \/\/ Rational Roots (Integers or Fractions)\n                html += `\n                <div class=\"step-card\">\n                    <div class=\"step-title\">Step 3: Find Roots (x)<\/div>\n                    <div class=\"explanation\">\n                        Since \u0394 is a perfect square (\u221a${delta} = ${sqrtDelta}), we use the quadratic formula:\n                    <\/div>\n                    <div class=\"math-block\">\n                        x = (-b \u00b1 \u221a\u0394) \/ 2a\n                    <\/div>\n                    <div class=\"explanation\">\n                        <strong>Root 1:<\/strong> x\u2081 = (${-b} - ${sqrtDelta}) \/ ${2*a} = ${-b - sqrtDelta} \/ ${2*a}<br>\n                        <strong>Root 2:<\/strong> x\u2082 = (${-b} + ${sqrtDelta}) \/ ${2*a} = ${-b + sqrtDelta} \/ ${2*a}\n                    <\/div>\n                <\/div>`;\n\n                \/\/ Calculate simplified fractions for roots\n                const r1 = simplifyFraction(-b - sqrtDelta, 2*a);\n                const r2 = simplifyFraction(-b + sqrtDelta, 2*a);\n\n                html += `\n                <div class=\"step-card\">\n                    <div class=\"step-title\">Step 4: Convert Roots to Factors<\/div>\n                    <div class=\"explanation\">\n                        Strategy: If x = <span class=\"fraction\"><span>n<\/span><span class=\"bottom\">d<\/span><\/span>, then the factor is (dx - n).\n                    <\/div>\n                    \n                    <hr style=\"border:0; border-top:1px dashed #eee; margin:10px 0;\">\n                    \n                    <div class=\"explanation\">\n                        <strong>For x\u2081:<\/strong><br>\n                        x = ${formatFractionHTML(r1.n, r1.d)} &rarr; (${formatFactorString(r1.d, r1.n)})\n                    <\/div>\n                    <br>\n                    <div class=\"explanation\">\n                        <strong>For x\u2082:<\/strong><br>\n                        x = ${formatFractionHTML(r2.n, r2.d)} &rarr; (${formatFactorString(r2.d, r2.n)})\n                    <\/div>\n                <\/div>`;\n\n                \/\/ Final Answer Logic\n                let factor1 = formatFactorString(r1.d, r1.n);\n                let factor2 = formatFactorString(r2.d, r2.n);\n                \n                \/\/ Check leading coefficient consistency\n                \/\/ The factors currently give leading coeff: r1.d * r2.d\n                \/\/ We need to match 'a'.\n                let currentA = r1.d * r2.d;\n                let scalar = a \/ currentA;\n                let finalStr = \"\";\n\n                if(scalar === 1) finalStr = `(${factor1})(${factor2})`;\n                else if(scalar === -1) finalStr = `-(${factor1})(${factor2})`;\n                else finalStr = `${scalar}(${factor1})(${factor2})`;\n                \n                \/\/ Clean up double parenthesis if factor is single term (rare in this logic but possible)\n                finalStr = finalStr.replace(\/\\(\\(\/g, \"(\").replace(\/\\)\\)\/g, \")\");\n\n                html += `<div class=\"final-answer\">${finalStr}<\/div>`;\n            }\n        }\n\n        solutionArea.style.display = 'block';\n        solutionArea.innerHTML = html;\n    }\n\n    \/\/ --- Helper Functions ---\n\n    function simplifyFraction(n, d) {\n        let gcd = Math.abs(getGCD(n, d));\n        n \/= gcd;\n        d \/= gcd;\n        \/\/ Ensure denominator is positive for standard form (dx - n)\n        if (d < 0) { n = -n; d = -d; }\n        return { n: n, d: d };\n    }\n\n    function formatFractionHTML(n, d) {\n        if (d === 1) return n;\n        return `<span class=\"fraction\"><span>${n}<\/span><span class=\"bottom\">${d}<\/span><\/span>`;\n    }\n\n    function formatFactorString(d, n) {\n        \/\/ Creates string \"dx - n\"\n        \/\/ Note: factor is (denominator * x - numerator)\n        \/\/ If x = 3\/2, then 2x = 3 -> 2x - 3\n        \n        let dStr = (d === 1) ? \"x\" : `${d}x`;\n        let nStr = \"\";\n        \n        \/\/ logic: factor is (dx - n). \n        \/\/ If n is positive (e.g. 3), we get (dx - 3)\n        \/\/ If n is negative (e.g. -5), we get (dx - (-5)) -> (dx + 5)\n        \n        if (n > 0) nStr = ` - ${Math.abs(n)}`;\n        else if (n < 0) nStr = ` + ${Math.abs(n)}`;\n        else nStr = \"\"; \/\/ n is 0\n\n        return `${dStr}${nStr}`;\n    }\n<\/script>\n\n<\/body>\n<\/html><\/div><\/div><div class=\"wpb_wrapper wpb_text_column td_block_wrap td_block_wrap vc_column_text tdi_9  tagdiv-type td-pb-border-top td_block_template_1\"  data-td-block-uid=\"tdi_9\" ><div class=\"td-block-title-wrap\"><\/div><div class=\"td-fix-index\"><h1 data-start=\"492\" data-end=\"563\"><strong data-start=\"494\" data-end=\"563\">User Guide: Factoring Trinomials Calculator\u00a0<\/strong><\/h1>\n<p data-start=\"565\" data-end=\"890\">The <strong data-start=\"569\" data-end=\"604\">Factoring Trinomials Calculator<\/strong> is a learning tool designed to help students and educators factor quadratic expressions of the form<\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">ax^2 + bx + c<\/annotation><\/semantics><\/math> into binomial factors <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>p<\/mi><mi>x<\/mi><mo>+<\/mo><mi>q<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(mx + n)(px + q)<\/annotation><\/semantics><\/math> Unlike simple calculators, this tool explains each step, helping users <strong data-start=\"838\" data-end=\"872\">understand the algebraic logic<\/strong> behind factoring.<\/p>\n<h2 data-start=\"897\" data-end=\"929\"><strong data-start=\"900\" data-end=\"929\">How to Use the Calculator<\/strong><\/h2>\n<h3 data-start=\"931\" data-end=\"961\">Input the Coefficients<\/h3>\n<p data-start=\"964\" data-end=\"1030\">Enter the values of <strong data-start=\"984\" data-end=\"989\">a<\/strong>, <strong data-start=\"991\" data-end=\"996\">b<\/strong>, and <strong data-start=\"1002\" data-end=\"1007\">c<\/strong> in the input fields.<\/p>\n<p data-start=\"1033\" data-end=\"1081\"><strong data-start=\"1033\" data-end=\"1038\">a<\/strong>: coefficient of\u00a0<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">x^2<\/annotation><\/semantics><\/math>\u00a0(cannot be zero)<\/p>\n<p data-start=\"1084\" data-end=\"1113\"><strong data-start=\"1084\" data-end=\"1089\">b<\/strong>: coefficient of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math>\u00a0<\/p>\n<p data-start=\"1116\" data-end=\"1138\"><strong data-start=\"1116\" data-end=\"1121\">c<\/strong>: constant term<\/p>\n<p data-start=\"1140\" data-end=\"1232\"><strong data-start=\"1140\" data-end=\"1148\">Tip:<\/strong> Include negative signs where needed (e.g., for <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>5<\/mn><mi>x<\/mi><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2 &#8211; 5x + 6<\/annotation><\/semantics><\/math> , enter <code data-start=\"1220\" data-end=\"1228\">b = -5<\/code>).<\/p>\n<h3 data-start=\"1239\" data-end=\"1272\">Click the \u201cFactor\u201d Button<\/h3>\n<p data-start=\"1273\" data-end=\"1360\">The calculator will perform <strong data-start=\"1301\" data-end=\"1324\">AC Splitting Method<\/strong> automatically, using this sequence:<\/p>\n<ol data-start=\"1362\" data-end=\"1857\">\n<li data-start=\"1362\" data-end=\"1440\">\n<p data-start=\"1365\" data-end=\"1440\"><strong data-start=\"1365\" data-end=\"1383\">Multiply a \u00d7 c<\/strong>: Finds the product of the first and last coefficients.\n<\/li>\n<li data-start=\"1441\" data-end=\"1518\">\n<p data-start=\"1444\" data-end=\"1518\"><strong data-start=\"1444\" data-end=\"1471\">Find two numbers (p, q)<\/strong>: These numbers multiply to a\u00d7c and add to b.\n<\/li>\n<li data-start=\"1519\" data-end=\"1603\">\n<p data-start=\"1522\" data-end=\"1603\"><strong data-start=\"1522\" data-end=\"1547\">Split the middle term<\/strong>: Rewrite<br \/>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">ax^2 + bx + c<\/annotation><\/semantics><\/math> as <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>p<\/mi><mi>x<\/mi><mo>+<\/mo><mi>q<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">ax^2 + px + qx + c<\/annotation><\/semantics><\/math>.<\/li>\n<li data-start=\"1604\" data-end=\"1744\">\n<p data-start=\"1607\" data-end=\"1744\"><strong data-start=\"1607\" data-end=\"1629\">Factor by grouping<\/strong>: Group the first two terms and last two terms, then factor out the greatest common factor (GCF) from each group.\n<\/li>\n<li data-start=\"1745\" data-end=\"1857\">\n<p data-start=\"1748\" data-end=\"1857\"><strong data-start=\"1748\" data-end=\"1782\">Factor out the common binomial<\/strong>: Combine the groups to get the final factored form<br \/>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>m<\/mi><mi>x<\/mi><mo>+<\/mo><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>p<\/mi><mi>x<\/mi><mo>+<\/mo><mi>q<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(mx + n)(px + q)<\/annotation><\/semantics><\/math>.<\/li>\n<\/ol>\n<h3 data-start=\"1864\" data-end=\"1898\">View Step-by-Step Solution<\/h3>\n<ul data-start=\"1899\" data-end=\"2132\">\n<li data-start=\"1899\" data-end=\"1982\">\n<p data-start=\"1901\" data-end=\"1982\">The <strong data-start=\"1905\" data-end=\"1928\">steps are displayed<\/strong> below the result, showing each calculation clearly.\n<\/li>\n<li data-start=\"1983\" data-end=\"2068\">\n<p data-start=\"1985\" data-end=\"2068\">Fractions are automatically simplified for neat algebraic form (e.g., 1.5 \u2192 3\/2).\n<\/li>\n<li data-start=\"2069\" data-end=\"2132\">\n<p data-start=\"2071\" data-end=\"2132\">All <strong data-start=\"2075\" data-end=\"2090\">+ \/ \u2212 signs<\/strong> are shown correctly to avoid confusion.\n<\/li>\n<\/ul>\n<h2 data-start=\"2139\" data-end=\"2156\"><strong data-start=\"2142\" data-end=\"2156\">Example<\/strong><\/h2>\n<p data-start=\"2158\" data-end=\"2188\"><strong data-start=\"2158\" data-end=\"2168\">Input:<\/strong><\/p>\n<p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>7<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x^2 + 7x + 4<\/annotation><\/semantics><\/math> \u00a0<\/p>\n<p data-start=\"2190\" data-end=\"2216\"><strong data-start=\"2190\" data-end=\"2216\">Step-by-Step Solution:<\/strong><\/p>\n<ol data-start=\"2217\" data-end=\"2513\">\n<li data-start=\"2217\" data-end=\"2248\">\n<p data-start=\"2220\" data-end=\"2248\">Multiply a \u00d7 c: 3 \u00d7 4 = 12\n<\/li>\n<li data-start=\"2249\" data-end=\"2313\">\n<p data-start=\"2252\" data-end=\"2313\">Find two numbers that multiply to 12 and sum to 7 \u2192 3 and 4\n<\/li>\n<li data-start=\"2314\" data-end=\"2364\">\n<p data-start=\"2317\" data-end=\"2364\">Split the middle term:<br \/>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x^2 + 3x + 4x + 4<\/annotation><\/semantics><\/math>\u00a0<\/li>\n<li data-start=\"2365\" data-end=\"2409\">\n<p data-start=\"2368\" data-end=\"2409\">Group terms:<br \/>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(3x^2 + 3x) + (4x + 4)<\/annotation><\/semantics><\/math>\u00a0<\/li>\n<li data-start=\"2410\" data-end=\"2458\">\n<p data-start=\"2413\" data-end=\"2458\">Factor each group:<br \/>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">3x(x + 1) + 4(x + 1)<\/annotation><\/semantics><\/math>\u00a0<\/li>\n<li data-start=\"2459\" data-end=\"2513\">\n<p data-start=\"2462\" data-end=\"2513\">Factor out common binomial:<br \/>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(3x + 4)(x + 1)<\/annotation><\/semantics><\/math>\u2705<\/li>\n<\/ol>\n<h2 data-start=\"2520\" data-end=\"2542\"><strong data-start=\"2523\" data-end=\"2542\">Tips &#038; Notes<\/strong><\/h2>\n<ul data-start=\"2544\" data-end=\"3014\">\n<li data-start=\"2544\" data-end=\"2673\">\n<p data-start=\"2546\" data-end=\"2673\"><strong data-start=\"2546\" data-end=\"2577\">Non-factorable expressions:<\/strong> If the calculator shows \u201cCannot factor using integers,\u201d the trinomial has no integer factors.\n<\/li>\n<li data-start=\"2674\" data-end=\"2769\">\n<p data-start=\"2676\" data-end=\"2769\"><strong data-start=\"2676\" data-end=\"2696\">Check GCF first:<\/strong> Always see if a, b, c share a common factor before factoring manually.\n<\/li>\n<li data-start=\"2770\" data-end=\"2890\">\n<p data-start=\"2772\" data-end=\"2890\"><strong data-start=\"2772\" data-end=\"2792\">Mobile-friendly:<\/strong> The calculator is optimized for phones: input fields stack vertically for easy single-hand use.\n<\/li>\n<li data-start=\"2891\" data-end=\"3014\">\n<p data-start=\"2893\" data-end=\"3014\"><strong data-start=\"2893\" data-end=\"2914\">Learning benefit:<\/strong> This step-by-step method helps students <strong data-start=\"2955\" data-end=\"2982\">see how factoring works<\/strong>, not just get the final answer.\n<\/li>\n<\/ul>\n<\/div><\/div><\/div><\/div><div class=\"vc_column tdi_11  wpb_column vc_column_container tdc-column td-pb-span4 td-is-sticky\">\n<style scoped>\n\n\/* custom css *\/\n.tdi_11{\r\n                    vertical-align: baseline;\r\n                }.tdi_11 > .wpb_wrapper,\r\n\t\t\t\t.tdi_11 > .wpb_wrapper > .tdc-elements{\r\n\t\t\t\t    display: block;\r\n\t\t\t\t}.tdi_11 > .wpb_wrapper > .tdc-elements{\r\n\t\t\t\t    width: 100%;\r\n\t\t\t\t}.tdi_11 > .wpb_wrapper > .vc_row_inner{\r\n\t\t\t\t    width: auto;\r\n\t\t\t\t}.tdi_11 > .wpb_wrapper{\r\n\t\t\t\t    width: auto;\r\n\t\t\t\t    height: auto;\r\n\t\t\t\t}\n<\/style><div class=\"wpb_wrapper\" data-sticky-offset=\"20\"><div class=\"td_block_wrap td_block_list_menu tdi_12 td-blm-display-vertical td-pb-border-top td_block_template_1 widget\"  data-td-block-uid=\"tdi_12\" >\n<style>\n\n\/* inline tdc_css att *\/\n\n.tdi_12{\npadding-top:20px !important;\n}\n\n<\/style>\n<style>\n\/* custom css *\/\n.td_block_list_menu ul{\r\n                  flex-wrap: wrap;\r\n                  margin-left: 12px;\r\n                }.td_block_list_menu ul li{\r\n\t\t\t\t\tmargin-left: 0;\r\n\t\t\t\t}.td_block_list_menu ul li a{\r\n\t\t\t\t\tdisplay: flex;\r\n                  \tmargin-left: 0;\r\n                }.td_block_list_menu .td-blm-menu-item-txt{\r\n\t\t\t\t\tdisplay: flex;\r\n\t\t\t\t\talign-items: center;\r\n\t\t\t\t\tflex-grow: 1;\r\n\t\t\t\t}.td_block_list_menu .sub-menu{\r\n                  padding-left: 22px;\r\n                }.td_block_list_menu .sub-menu li{\r\n                  font-size: 13px;\r\n                }.td_block_list_menu li.current-menu-item > a,\r\n\t\t\t\t.td_block_list_menu li.current-menu-ancestor > a,\r\n\t\t\t\t.td_block_list_menu li.current-category-ancestor > a{\r\n\t\t\t\t    color: #4db2ec;\r\n\t\t\t\t}.td_block_list_menu .td-blm-sub-icon{\r\n\t\t\t\t\tdisplay: flex;\r\n\t\t\t\t\talign-items: center;\r\n\t\t\t\t\tjustify-content: center;\r\n\t\t\t\t\tmargin-left: .6em;\r\n\t\t\t\t\tpadding: 0 .6em;\r\n\t\t\t\t\ttransition: transform .2s ease-in-out;\r\n\t\t\t\t}.td_block_list_menu .td-blm-sub-icon svg{\r\n\t\t\t\t\tdisplay: block;\r\n\t\t\t\t\twidth: 1em;\r\n\t\t\t\t\theight: auto;\r\n\t\t\t\t}.td_block_list_menu .td-blm-sub-icon svg,\r\n\t\t\t\t.td_block_list_menu .td-blm-sub-icon svg *{\r\n\t\t\t\t\tfill: currentColor;\r\n\t\t\t\t}.td_block_list_menu.td-blm-display-accordion .menu-item-has-children ul{\r\n\t\t\t\t\tdisplay: none;\r\n\t\t\t\t}.td_block_list_menu.td-blm-display-accordion .menu-item-has-children-open > a > .td-blm-sub-icon{\r\n\t\t\t\t\ttransform: rotate(180deg);\r\n\t\t\t\t}.td_block_list_menu.td-blm-display-horizontal ul{\r\n\t\t\t\t\tdisplay: flex;\r\n\t\t\t\t}body .tdi_12 ul{\r\n\t\t\t\t\ttext-align: left;\r\n\t\t\t\t\tjustify-content: flex-start;\r\n\t\t\t\t}body .tdi_12 ul li a{\r\n\t\t\t\t\tjustify-content: flex-start;\r\n\t\t\t\t}body .tdi_12 .td-blm-menu-item-txt{\r\n\t\t\t\t\tflex-grow: 1;\r\n\t\t\t\t}\n<\/style><div class=\"td-block-title-wrap\"><h4 class=\"block-title td-block-title\"><span class=\"td-pulldown-size\">Math Calculators<\/span><\/h4><\/div><div id=tdi_12 class=\"td_block_inner td-fix-index\"><div class=\"menu-math-container\"><ul id=\"menu-math\" class=\"menu\"><li id=\"menu-item-3614\" class=\"menu-item menu-item-type-post_type 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[]).push({});\n<\/script><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":8712,"parent":3595,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-8694","page","type-page","status-publish","has-post-thumbnail"],"rankMath":{"parentDomain":"ezcalculatoronline.com","noFollowDomains":[],"noFollowExcludeDomains":[],"noFollowExternalLinks":false,"featuredImageNotice":"The featured image should be at least 200 by 200 pixels to be picked up by Facebook and other social media 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