Find the linear factors of $\displaystyle 6 + 5x - 2x^2 - x^3$
first look here:
Rational root theorem - Wikipedia, the free encyclopedia
now armed with this new knowledge we can see that x = -1 is a possible root of the polynomial, and after substituting it in the polynomial we see that it's indeed a root, now all we have to do is reduce the polynomial to second degree by long division
The rational root theorem tell us that if this has a linear factor with rational
coeficients it is one of: $\displaystyle (x \pm 1),\ (x \pm 2),\ (x \pm 3),\ (x \pm 6)$.
Working our way through these shows that $\displaystyle (x+1)$ is in fact a factor and:
$\displaystyle 6 + 5x - 2x^2 - x^3=(x+1)(-x^2-x+6)$
and the quadratic you can deal with using the quadratic formula.
RonL