A. Mark for Review Which expression is equivalent to 28x^3+2x^2+9x A 28x(x^2+2x+9) D 2x(2x^3+2x^2+1) A x(28x^2+2x+9) D 34(x^3+x^2+x)

To determine which expression is equivalent to \( 28x^3 + 2x^2 + 9x \), we need to factorize the given expression and compare it with the options.<br /><br />### Step 1: Factor out the greatest common factor (GCF)<br />The terms in the expression are \( 28x^3 \), \( 2x^2 \), and \( 9x \). The GCF of these terms is \( x \), as all terms contain at least one \( x \).<br /><br />Factoring out \( x \):<br />\[<br />28x^3 + 2x^2 + 9x = x(28x^2 + 2x + 9)<br />\]<br /><br />### Step 2: Compare with the options<br />Now, let's analyze each option:<br /><br />- **Option A:** \( 28x(x^2 + 2x + 9) \) <br /> This is incorrect because factoring \( x \) from the original expression leaves \( 28x^2 + 2x + 9 \), not \( x^2 + 2x + 9 \).<br /><br />- **Option B:** \( 2x(2x^3 + 2x^2 + 1) \) <br /> This is incorrect because factoring \( 2x \) does not produce the correct terms. For example, dividing \( 28x^3 \) by \( 2x \) gives \( 14x^2 \), not \( 2x^3 \).<br /><br />- **Option C:** \( x(28x^2 + 2x + 9) \) <br /> This is correct because factoring \( x \) from \( 28x^3 + 2x^2 + 9x \) results in \( x(28x^2 + 2x + 9) \).<br /><br />- **Option D:** \( 34(x^3 + x^2 + x) \) <br /> This is incorrect because the coefficients do not match the original expression. For example, the coefficient of \( x^3 \) in the original expression is \( 28 \), not \( 34 \).<br /><br />### Final Answer:<br />The correct option is:<br />\[<br />\boxed{\text{C } x(28x^2 + 2x + 9)}<br />\]