# A polynomial function f(x) with integer coefficients has a leading coefficient of -24 and a constant term of 1. State the possible roots of f(x)? Please include details. Thanks!

Jan 31, 2018

$\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$

#### Explanation:

We can use the rational root theorem.

Leading coefficient: $- 24$ and constant term $1$.

All possible values of $p$ are $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$, which are the factors of the leading coefficient.

All factors of $q = \pm 1$, which are the only possible factors of the constant term.

The theorem says that any rational root of $f \left(x\right)$ will be of the form $\frac{p}{q}$

The possible roots of $f \left(x\right)$ are therefore: $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$. This is a little easier than usual since the constant term was 1.