<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
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    }
  </style>
</head>
<body>

  <div class="grid-container">
    
    <div class="column col-degree">
      <div class="column-header">
        <span>⚡ By Degree (Highest Power)</span>
      </div>
      <div class="card-list">
        <div class="item-card">
          <span class="badge-count">0</span>
          <span class="name-badge">Constant</span>
          <span class="example-math">7</span>
        </div>
        <div class="item-card">
          <span class="badge-count">1</span>
          <span class="name-badge">Linear</span>
          <span class="example-math">2x + 1</span>
        </div>
        <div class="item-card">
          <span class="badge-count">2</span>
          <span class="name-badge">Quadratic</span>
          <span class="example-math">3x<sup>2</sup> − 5</span>
        </div>
        <div class="item-card">
          <span class="badge-count">3</span>
          <span class="name-badge">Cubic</span>
          <span class="example-math">x<sup>3</sup></span>
        </div>
        <div class="item-card">
          <span class="badge-count">4</span>
          <span class="name-badge">Quartic</span>
          <span class="example-math">5x<sup>4</sup> − 2x</span>
        </div>
      </div>
    </div>

    
    <div class="column col-terms">
      <div class="column-header">
        <span>🔢 By Number of Terms</span>
      </div>
      <div class="card-list">
        <div class="item-card">
          <span class="badge-count">1</span>
          <span class="name-badge">Monomial</span>
          <span class="example-math">−8x<sup>2</sup></span>
        </div>
        <div class="item-card">
          <span class="badge-count">2</span>
          <span class="name-badge">Binomial</span>
          <span class="example-math">4x + 3</span>
        </div>
        <div class="item-card">
          <span class="badge-count">3</span>
          <span class="name-badge">Trinomial</span>
          <span class="example-math">x<sup>2</sup> + 5x − 6</span>
        </div>
        <div class="item-card">
          <span class="badge-count">4+</span>
          <span class="name-badge">Polynomial</span>
          <span class="example-math">x<sup>3</sup> − 2x<sup>2</sup> + 3x − 1</span>
        </div>
      </div>
    </div>
  </div>

</body>
</html>

Understanding Polynomial Functions and Their Degrees

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Simplifying and Classifying Polynomials</title>
  <style>
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      font-weight: 700;
      font-size: 14px;
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      justify-content: center;
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      opacity: 1;
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      align-items: center;
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    sup {
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      max-width: 420px;
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      font-size: 20px;
      font-weight: 800;
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      font-size: 22px;
      font-weight: 800;
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      box-shadow: 0 4px 12px rgba(37, 99, 235, 0.25);
      letter-spacing: 0.5px;
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      justify-content: center;
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      font-weight: 600;
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      color: #475569;
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      gap: 8px;
      align-items: center;
      justify-content: center;
      width: 100%;
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      border: 1px solid #cbd5e1;
      color: #334155;
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      .prop-val {
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      .prop-lbl {
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  </style>
</head>
<body>

  <div class="main-wrapper">
    
    <div class="stepper-nav">
      <button class="step-btn active" data-idx="0" aria-label="Step 1">1</button>
      <div class="nav-line"></div>
      <button class="step-btn" data-idx="1" aria-label="Step 2">2</button>
      <div class="nav-line"></div>
      <button class="step-btn" data-idx="2" aria-label="Step 3">3</button>
      <div class="nav-line"></div>
      <button class="step-btn" data-idx="3" aria-label="Step 4">4</button>
    </div>

    
    <div class="step-title" id="stepTitle">Step 1: Combine Like Terms</div>

    
    <div class="stage-container">

      
      <div class="step-card active" id="card0">
        <div class="math-row">
          <span class="term-linear">8x</span>
          <span class="term-cubic">- 5x<sup>3</sup></span>
          <span class="term-const">+ 12</span>
          <span class="term-cubic">+ 2x<sup>3</sup></span>
          <span class="term-const">- 4</span>
        </div>
        <div class="arrow-down">↓</div>
        <div class="highlight-box">
          <div class="math-row">
            <span class="term-cubic">(-5 + 2)x<sup>3</sup></span>
            <span class="term-linear">+ 8x</span>
            <span class="term-const">+ (12 - 4)</span>
          </div>
        </div>
      </div>

      
      <div class="step-card" id="card1">
        <div class="math-row" style="color: #64748b; font-size: 13px;">
          Highest Power → Lowest Power
        </div>
        <div class="highlight-box" style="border-color: #38bdf8; background: #f0f9ff;">
          <div class="math-expr">P(x) = -3x<sup>3</sup> + 8x + 8</div>
        </div>
        <div class="math-row" style="font-size: 12px; gap: 6px;">
          <span class="term-cubic">Degree 3</span>
          <span class="term-linear">Degree 1</span>
          <span class="term-const">Degree 0</span>
        </div>
      </div>

      
      <div class="step-card" id="card2">
        <div class="prop-grid">
          <div class="prop-item">
            <div class="prop-val">3</div>
            <div class="prop-lbl">Degree</div>
          </div>
          <div class="prop-item">
            <div class="prop-val">-3</div>
            <div class="prop-lbl">Lead Coeff.</div>
          </div>
          <div class="prop-item">
            <div class="prop-val">3</div>
            <div class="prop-lbl">Terms</div>
          </div>
        </div>
        <div class="highlight-box" style="font-size: 13px; color: #475569; font-weight: 600;">
          Highest Exponent: <b>3</b> &nbsp;|&nbsp; Coefficient: <b>-3</b>
        </div>
      </div>

      
      <div class="step-card" id="card3">
        <div class="name-badge">Cubic Trinomial</div>
        <div class="breakdown-row">
          <div class="breakdown-tag">Degree 3 &rarr; <b>Cubic</b></div>
          <div class="breakdown-tag">3 Terms &rarr; <b>Trinomial</b></div>
        </div>
      </div>

    </div>

    
    <div class="ctrl-row">
      <button class="btn-ctrl" id="prevBtn" aria-label="Previous step">&larr; Prev</button>
      <button class="btn-ctrl" id="playBtn" aria-label="Toggle autoplay">⏸ Pause</button>
      <button class="btn-ctrl" id="nextBtn" aria-label="Next step">Next &rarr;</button>
    </div>
  </div>

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</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
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      font-size: 13px;
      color: #334155;
      font-weight: 600;
    }
  </style>
</head>
<body>
  <div class="grid">
    
    <div class="col">
      <div class="badge badge-valid">✓ Valid Polynomial</div>
      
      <div class="math-stage" id="polyMain">
        
      </div>

      <div class="tag-row">
        <div class="tag-card card-exp" id="cardExp">
          <span class="tag-pill pill-emerald">Powers: 3, 2</span>
          <span class="desc">Whole numbers (0, 1, 2...)</span>
        </div>
        <div class="tag-card card-coef" id="cardCoef">
          <span class="tag-pill pill-blue">Coefficients: 5, −4</span>
          <span class="desc">Real numbers</span>
        </div>
        <div class="tag-card card-const" id="cardConst">
          <span class="tag-pill pill-violet">Constant: +7</span>
          <span class="desc">Degree 0 term (7x⁰)</span>
        </div>
      </div>
    </div>

    
    <div class="col">
      <div class="badge badge-invalid">✗ Not a Polynomial</div>
      
      <div class="tag-row">
        <div class="violation-card" id="v1">
          <div class="violation-math" id="mathV1"></div>
          <div class="violation-info">
            <span class="tag-pill pill-rose">Negative power</span>
            <span class="desc">−2 is not &ge; 0</span>
          </div>
        </div>

        <div class="violation-card" id="v2">
          <div class="violation-math" id="mathV2"></div>
          <div class="violation-info">
            <span class="tag-pill pill-rose">Variable in denominator</span>
            <span class="equiv" id="equivV2"></span>
          </div>
        </div>

        <div class="violation-card" id="v3">
          <div class="violation-math" id="mathV3"></div>
          <div class="violation-info">
            <span class="tag-pill pill-rose">Radical / Fraction power</span>
            <span class="equiv" id="equivV3"></span>
          </div>
        </div>
      </div>
    </div>
  </div>

  <script>
    // Universal tap/click handler for mobile and desktop
    function onTap(element, callback) {
      if (!element) return;
      element.addEventListener('click', callback);
    }

    function renderMath() {
      const polyEl = document.getElementById('polyMain');
      const v1El = document.getElementById('mathV1');
      const v2El = document.getElementById('mathV2');
      const eq2El = document.getElementById('equivV2');
      const v3El = document.getElementById('mathV3');
      const eq3El = document.getElementById('equivV3');

      if (typeof katex !== 'undefined') {
        katex.render("5x^3 - 4x^2 + 7", polyEl, { displayMode: true });
        katex.render("3x^{-2}", v1El);
        katex.render("\\frac{4}{x}", v2El);
        katex.render("= 4x^{-1}", eq2El);
        katex.render("2\\sqrt{x}", v3El);
        katex.render("= 2x^{1/2}", eq3El);
      } else {
        polyEl.innerHTML = '<span style="font-family: serif; font-size: 22px;">5x³ − 4x² + 7</span>';
        v1El.innerHTML = '<span style="font-family: serif;">3x⁻²</span>';
        v2El.innerHTML = '<span style="font-family: serif;">4/x</span>';
        eq2El.innerHTML = '<span style="font-family: serif;">= 4x⁻¹</span>';
        v3El.innerHTML = '<span style="font-family: serif;">2√x</span>';
        eq3El.innerHTML = '<span style="font-family: serif;">= 2x<sup>1/2</sup></span>';
      }
    }

    renderMath();

    // Left Column Interactivity
    const leftCards = [
      { id: 'cardExp', cls: 'highlight-exp' },
      { id: 'cardCoef', cls: 'highlight-coef' },
      { id: 'cardConst', cls: 'highlight-const' }
    ];

    const polyStage = document.getElementById('polyMain');

    leftCards.forEach(item => {
      const el = document.getElementById(item.id);
      if (el) {
        onTap(el, () => {
          const isCurrentlyActive = el.classList.contains('active');
          // Reset all left cards
          leftCards.forEach(other => {
            const otherEl = document.getElementById(other.id);
            if (otherEl) otherEl.classList.remove('active');
            if (polyStage) polyStage.classList.remove(other.cls);
          });

          if (!isCurrentlyActive) {
            el.classList.add('active');
            if (polyStage) polyStage.classList.add(item.cls);
          }
        });
      }
    });

    // Right Column Interactivity
    const rightCards = ['v1', 'v2', 'v3'];
    rightCards.forEach(id => {
      const el = document.getElementById(id);
      if (el) {
        onTap(el, () => {
          const isCurrentlyActive = el.classList.contains('active');
          rightCards.forEach(cid => {
            const otherEl = document.getElementById(cid);
            if (otherEl) otherEl.classList.remove('active');
          });
          if (!isCurrentlyActive) {
            el.classList.add('active');
          }
        });
      }
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px 8px;
    }

    .toolbar {
      display: flex;
      gap: 8px;
      margin-bottom: 20px;
    }

    .btn {
      appearance: none;
      border: 1px solid #d1d5db;
      background: #ffffff;
      color: #4b5563;
      padding: 6px 14px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0,0,0,0.05);
      transition: all 0.25s ease;
    }

    .btn.active {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
      box-shadow: 0 2px 4px rgba(30,41,69,0.2);
    }

    .stage {
      position: relative;
      width: 100%;
      max-width: 480px;
      height: 70px;
      margin-bottom: 24px;
    }

    .term {
      position: absolute;
      top: 0;
      width: 30%;
      height: 64px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 24px;
      font-weight: 700;
      font-family: "Cambria Math", "Times New Roman", serif;
      border-radius: 12px;
      transition: transform 0.6s cubic-bezier(0.34, 1.3, 0.64, 1), box-shadow 0.3s ease;
      cursor: pointer;
      user-select: none;
    }

    .term sup {
      font-size: 16px;
      margin-left: 1px;
    }

    /* Term Colors */
    .term-cubic {
      background: #ede9fe;
      color: #5b21b6;
      border: 2px solid #c4b5fd;
    }

    .term-linear {
      background: #e0f2fe;
      color: #0369a1;
      border: 2px solid #7dd3fc;
    }

    .term-const {
      background: #fef3c7;
      color: #92400e;
      border: 2px solid #fde68a;
    }

    /* Positions: Given (4, -6x^3, +2x) */
    .pos-given-0 { transform: translateX(3%); }
    .pos-given-1 { transform: translateX(116%); }
    .pos-given-2 { transform: translateX(230%); }

    /* Positions: Standard (-6x^3, +2x, +4) */
    .pos-std-0 { transform: translateX(3%); }
    .pos-std-1 { transform: translateX(116%); }
    .pos-std-2 { transform: translateX(230%); }

    /* Cards Grid */
    .callout-grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 10px;
      width: 100%;
      max-width: 480px;
    }

    .callout-card {
      border-radius: 10px;
      padding: 10px 8px;
      text-align: center;
      display: flex;
      flex-direction: column;
      gap: 6px;
      transition: opacity 0.4s ease, transform 0.4s ease;
    }

    .card-cubic {
      background: #faf5ff;
      border: 1px solid #ddd6fe;
    }

    .card-linear {
      background: #f0f9ff;
      border: 1px solid #bae6fd;
    }

    .card-const {
      background: #fffbeb;
      border: 1px solid #fef08a;
    }

    .badge {
      display: inline-block;
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 3px 6px;
      border-radius: 6px;
    }

    .badge-cubic { background: #8b5cf6; color: #ffffff; }
    .badge-linear { background: #0ea5e9; color: #ffffff; }
    .badge-const { background: #f59e0b; color: #ffffff; }

    .tag-row {
      display: flex;
      flex-direction: column;
      gap: 3px;
      font-size: 13px;
      font-weight: 600;
      color: #374151;
    }

    .tag-val {
      font-size: 13px;
      color: #4b5563;
    }

    .arrow-indicator {
      font-size: 18px;
      line-height: 1;
      margin-bottom: 2px;
    }
  </style>
</head>
<body>

  <div class="toolbar">
    <button id="btnGiven" class="btn" onclick="setMode('given')">Original</button>
    <button id="btnStandard" class="btn active" onclick="setMode('standard')">Standard Form</button>
  </div>

  <div class="stage">
    
    <div id="termCubic" class="term term-cubic pos-std-0" onclick="setMode(currentMode === 'given' ? 'standard' : 'given')">
      -6x<sup>3</sup>
    </div>
    
    <div id="termLinear" class="term term-linear pos-std-1" onclick="setMode(currentMode === 'given' ? 'standard' : 'given')">
      +2x
    </div>
    
    <div id="termConst" class="term term-const pos-std-2" onclick="setMode(currentMode === 'given' ? 'standard' : 'given')">
      +4
    </div>
  </div>

  <div class="callout-grid">
    
    <div class="callout-card card-cubic">
      <div class="arrow-indicator" style="color:#8b5cf6;">▲</div>
      <div><span class="badge badge-cubic">Leading Term</span></div>
      <div class="tag-row">
        <span>Degree: 3</span>
        <span class="tag-val">Coeff: -6</span>
      </div>
    </div>

    
    <div class="callout-card card-linear">
      <div class="arrow-indicator" style="color:#0ea5e9;">▲</div>
      <div><span class="badge badge-linear">Linear Term</span></div>
      <div class="tag-row">
        <span>Degree: 1</span>
        <span class="tag-val">Coeff: +2</span>
      </div>
    </div>

    
    <div class="callout-card card-const">
      <div class="arrow-indicator" style="color:#f59e0b;">▲</div>
      <div><span class="badge badge-const">Constant</span></div>
      <div class="tag-row">
        <span>Degree: 0</span>
        <span class="tag-val">Value: +4</span>
      </div>
    </div>
  </div>

  <script>
    let currentMode = 'standard';
    const termCubic = document.getElementById('termCubic');
    const termLinear = document.getElementById('termLinear');
    const termConst = document.getElementById('termConst');
    const btnGiven = document.getElementById('btnGiven');
    const btnStandard = document.getElementById('btnStandard');

    function setMode(mode) {
      currentMode = mode;
      if (mode === 'given') {
        btnGiven.classList.add('active');
        btnStandard.classList.remove('active');

        termConst.className = 'term term-const pos-given-0';
        termConst.innerHTML = '4';

        termCubic.className = 'term term-cubic pos-given-1';
        termLinear.className = 'term term-linear pos-given-2';
      } else {
        btnStandard.classList.add('active');
        btnGiven.classList.remove('active');

        termCubic.className = 'term term-cubic pos-std-0';
        termLinear.className = 'term term-linear pos-std-1';

        termConst.className = 'term term-const pos-std-2';
        termConst.innerHTML = '+4';
      }
    }
  </script>
</body>
</html>

OGM.10.ALG.2

Aligned learning resources

Related diagrams