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 first look for the greatest common factor (GCF) of the terms. The GCF of the coefficients \(-14\), \(-7\), and \(-35\) is \(-7\). Additionally, the common variable among all the terms is \(x\). Thus, we can factor out \(-7x\): \[ -7x(2 + y + 5x) \text{ .} \] Now, let's express the remaining trinomial part clearly as \(2 + y + 5x\) in the parentheses, showcasing the factored form! To check if you've made common mistakes while factoring, remember to always verify that all terms were included and that the GCF was correctly identified. It’s also handy to double-check by redistributing to ensure you land back at the original polynomial. Happy factoring!