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

We begin with the polynomial: \[ 14 x^{4}+21 x^{3}+28 x \] **Step 1: Identify the greatest common factor (GCF).** - For the coefficients \(14\), \(21\), and \(28\), the GCF is \(7\). - For the variable part, the smallest power of \(x\) present is \(x\). Thus, the GCF is \(7x\). **Step 2: Factor out \(7x\).** Divide each term by \(7x\): - \(\displaystyle \frac{14x^4}{7x} = 2x^3\) - \(\displaystyle \frac{21x^3}{7x} = 3x^2\) - \(\displaystyle \frac{28x}{7x} = 4\) So, we have: \[ 14 x^{4}+21 x^{3}+28 x = 7x(2x^3+3x^2+4) \] **Step 3: Check the factorization by multiplication.** Multiply \(7x\) by each term in the parentheses: \[ 7x \cdot 2x^3 = 14x^4, \] \[ 7x \cdot 3x^2 = 21x^3, \] \[ 7x \cdot 4 = 28x. \] Adding these gives the original polynomial: \[ 14x^4 + 21x^3 + 28x. \] Thus, the factorization is correct. The final factorization is: \[ 14 x^{4}+21 x^{3}+28 x = 7x(2x^3+3x^2+4) \]