<h3>Quadratic expressions</h3><p>A <strong>quadratic</strong> has the form <code>ax^2 + bx + c</code> where the highest power is 2. To <strong>expand</strong> <code>(x + 2)(x + 3)</code> multiply every pair of terms to get <code>x^2 + 5x + 6</code>.</p><h3>Factorising</h3><p>To <strong>factorise</strong> <code>x^2 + 5x + 6</code>, find two numbers that multiply to 6 and add to 5 (these are 2 and 3), giving <code>(x + 2)(x + 3)</code>.</p><h3>Solving quadratic equations</h3><p>A <strong>quadratic equation</strong> is set equal to zero. To solve <code>x^2 + 5x + 6 = 0</code>, factorise then set each factor to zero: <code>x + 2 = 0</code> or <code>x + 3 = 0</code>, so <code>x = -2</code> or <code>x = -3</code>. These are the <strong>roots</strong>.</p><div class="callout"><strong>Kenyan context:</strong> A rectangular shamba is 3 m longer than it is wide and has an area of 40 square metres. If the width is x, then <code>x(x + 3) = 40</code>, which becomes <code>x^2 + 3x - 40 = 0</code>. Factorising gives <code>(x + 8)(x - 5) = 0</code>, so x = 5 m (we ignore the negative). The shamba is 5 m by 8 m.</div>