Which of the following are factors of 3x+3x^2 Choose all answers that apply: A x(x+1) B 3(x+1) 3x^2

To determine which of the given options are factors of \(3x + 3x^2\), we first factor the expression.<br /><br />The expression \(3x + 3x^2\) can be factored by factoring out the greatest common factor (GCF):<br /><br />\[ 3x + 3x^2 = 3x(1 + x) \]<br /><br />Now, let's check each option to see if it is a factor of \(3x(1 + x)\):<br /><br />A. \(x(x+1)\)<br /><br />We can rewrite \(x(x+1)\) as:<br />\[ x(x+1) = x \cdot (x+1) \]<br /><br />Since \(3x(1 + x) = 3x(x+1)\), we see that \(x(x+1)\) is indeed a factor.<br /><br />B. \(3(x+1)\)<br /><br />We can rewrite \(3(x+1)\) as:<br />\[ 3(x+1) = 3 \cdot (x+1) \]<br /><br />Since \(3x(1 + x) = 3x(x+1)\), we see that \(3(x+1)\) is also a factor.<br /><br />C. \(3x^2\)<br /><br />We can rewrite \(3x^2\) as:<br />\[ 3x^2 = 3 \cdot x^2 \]<br /><br />Since \(3x(1 + x) = 3x(x+1)\), we see that \(3x^2\) is not a factor because it does not include the \((x+1)\) term.<br /><br />Therefore, the correct answers are:<br />A. \(x(x+1)\)<br />B. \(3(x+1)\)