Remove the largest possible common factor. Check your answer by multiplication \[ 14 x^{4}+21 x^{3}+28 x \] Factor out the greatest common factor. \( 14 x^{4}+21 x^{3}+28 x=\square \)

First, identify the greatest common factor (GCF) of the coefficients and the variable parts: 1. The coefficients \(14\), \(21\), and \(28\) share a common factor of \(7\). 2. The variable part \(x^4\), \(x^3\), and \(x\) have a common factor of \(x\). Thus, the GCF is \(7x\). Now, factor \(7x\) out of each term: \[ \begin{aligned} 14x^4 &= 7x(2x^3),\\[5mm] 21x^3 &= 7x(3x^2),\\[5mm] 28x &= 7x(4). \end{aligned} \] So the expression becomes: \[ 14x^4 + 21x^3 + 28x = 7x\left(2x^3 + 3x^2 + 4\right). \] To verify by multiplication, distribute \(7x\): \[ 7x \cdot 2x^3 = 14x^4,\quad 7x \cdot 3x^2 = 21x^3,\quad 7x \cdot 4 = 28x. \] Each term matches the original expression. Thus, the factorization is: \[ 14x^4 + 21x^3 + 28x = 7x\left(2x^3 + 3x^2 + 4\right). \]