Question

How do you factor `x^2-26x^3-27`?

Answer 1

Factoring a polynomial (when possible using real numbers) means to find its roots, and then divide the polynomial for the linear factor `(x-x_i)`, where `x_i` is the root.

In your case, you can see that `x=-1` is a root, since
`(-1)^2 -26(-1)^3-27=1+26-27=0`.

Dividing your polynomial by `(x+1)`, you obtain `-(26x^2-27x+27)`. The discriminant of this quadratic polynomial is `-2079`, and thus it has no real solutions. We cannot further simplify it, and so the answer is
`-(x+1)(26x^2-27x+27)`