Factor the given polynomial by finding the greatest common monomial factor (or the negative of the \[ -14 x-7 x y-35 x^{2} \]

To factor the polynomial \(-14x - 7xy - 35x^2\), we will first identify the greatest common monomial factor (GCMF) of the terms. 1. **Identify the coefficients**: The coefficients of the terms are \(-14\), \(-7\), and \(-35\). 2. **Find the GCF of the coefficients**: The GCF of \(-14\), \(-7\), and \(-35\) is \(7\). 3. **Identify the variable factors**: The variable factors in the terms are \(x\), \(xy\), and \(x^2\). The common variable factor is \(x\). 4. **Combine the GCF of the coefficients and the variable factors**: The GCMF is \(7x\). Now, we can factor out \(7x\) from each term: \[ -14x = -7x \cdot 2 \] \[ -7xy = -7x \cdot y \] \[ -35x^2 = -7x \cdot 5x \] Now we can rewrite the polynomial: \[ -14x - 7xy - 35x^2 = -7x(2 + y + 5x) \] Thus, the factored form of the polynomial is: \[ -7x(2 + y + 5x) \]