Question

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

Answer 1

This actually requires factoring by grouping. Let's group the function like this: `(3x^3+x^2)-(75x+25)`. We then factor the two groups to get `x^2(3x+1)-25(3x+1)`. The common factor between the two groups is `(3x+1)`, which we factor out to get `(3x+1)(x^2-25)`.

Now, we notice that `x^2-25=(x+5)(x-5)` (using the difference between squares identity).

Thus, our final answer is `(3x+1)(x+5)(x-5)`