# How do you factor 3x^3+x^2-75x-25?

This actually requires factoring by grouping. Let's group the function like this: $\left(3 {x}^{3} + {x}^{2}\right) - \left(75 x + 25\right)$. We then factor the two groups to get ${x}^{2} \left(3 x + 1\right) - 25 \left(3 x + 1\right)$. The common factor between the two groups is $\left(3 x + 1\right)$, which we factor out to get $\left(3 x + 1\right) \left({x}^{2} - 25\right)$.
Now, we notice that ${x}^{2} - 25 = \left(x + 5\right) \left(x - 5\right)$ (using the difference between squares identity).
Thus, our final answer is $\left(3 x + 1\right) \left(x + 5\right) \left(x - 5\right)$