J) SA Divide. Write your answer in simplest form. (2k^2-32)/(k^2)div 3 square

To divide the given expression, we need to follow the steps below:<br /><br />1. Rewrite the division as multiplication by the reciprocal.<br />2. Factor the numerator if possible.<br />3. Cancel out common factors.<br />4. Simplify the resulting expression.<br /><br />Given expression:<br />\[<br />\frac{2k^2 - 32}{k^2} \div 3<br />\]<br /><br />Step 1: Rewrite the division as multiplication by the reciprocal.<br />\[<br />\frac{2k^2 - 32}{k^2} \times \frac{1}{3}<br />\]<br /><br />Step 2: Factor the numerator if possible.<br />\[<br />2k^2 - 32 = 2(k^2 - 16)<br />\]<br />So the expression becomes:<br />\[<br />\frac{2(k^2 - 16)}{k^2} \times \frac{1}{3}<br />\]<br /><br />Step 3: Cancel out common factors.<br />There are no common factors to cancel in this case.<br /><br />Step 4: Simplify the resulting expression.<br />\[<br />\frac{2(k^2 - 16)}{k^2} \times \frac{1}{3} = \frac{2(k^2 - 16)}{3k^2}<br />\]<br /><br />Thus, the simplified form of the given expression is:<br />\[<br />\boxed{\frac{2(k^2 - 16)}{3k^2}}<br />\]