Find the linear factors of $\displaystyle 6 + 5x - 2x^2 - x^3$

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- Feb 17th 2008, 10:30 PMnerdzorLinear factors of polynomial
Find the linear factors of $\displaystyle 6 + 5x - 2x^2 - x^3$

- Feb 17th 2008, 10:58 PMPeritus
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 - Feb 17th 2008, 11:03 PMCaptainBlack
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