Select the simplified form of this expression \[ \frac{x^{4}+2 x^{3}}{14 x+28} \]

To simplify the expression \( \frac{x^{4}+2 x^{3}}{14 x+28} \), we start by factoring both the numerator and the denominator. 1. The numerator can be factored as follows: \[ x^4 + 2x^3 = x^3(x + 2) \] 2. The denominator can be factored out by taking out the common factor: \[ 14x + 28 = 14(x + 2) \] Now we can rewrite the original expression: \[ \frac{x^3(x + 2)}{14(x + 2)} \] Since \(x + 2\) appears in both the numerator and the denominator, we can cancel it out (as long as \(x + 2 \neq 0\)) to get: \[ \frac{x^3}{14} \] Therefore, the simplified form of the expression is: \[ \frac{x^3}{14} \]