# Linear factors of polynomial

• February 17th 2008, 10:30 PM
nerdzor
Linear factors of polynomial
Find the linear factors of $6 + 5x - 2x^2 - x^3$
• February 17th 2008, 10:58 PM
Peritus
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
• February 17th 2008, 11:03 PM
CaptainBlack
Quote:

Originally Posted by nerdzor
Find the linear factors of $6 + 5x - 2x^2 - x^3$

The rational root theorem tell us that if this has a linear factor with rational
coeficients it is one of: $(x \pm 1),\ (x \pm 2),\ (x \pm 3),\ (x \pm 6)$.

Working our way through these shows that $(x+1)$ is in fact a factor and:

$6 + 5x - 2x^2 - x^3=(x+1)(-x^2-x+6)$

and the quadratic you can deal with using the quadratic formula.

RonL