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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

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

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