# Better ways to find factors of polynomials with degrees more than 3?

Let's say there's a polynomial $p(x)$. And let's also suppose you try a value $t$ for $x$ and find that $x - t$ is a factor (using the factor theorem).

So now comes my question: Is there a better/faster way to find the other factor other than long division? I could divide $x - t$ from $p(x)$ and find the other factor and so on, but it becomes quite tedious as the degree of the polynomial you are dealing with increases.

Thanks

• When $\deg f\ge4$, there may be quadratic factor even if there are no linear factors. – Lord Shark the Unknown Sep 16 '18 at 9:50
• Do you mean to find the factors without knowing the roots? – dmtri Sep 16 '18 at 10:12
• @dmtri Yes. Exactly. – Ramana Sep 16 '18 at 12:19