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!

1 Answer
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(x) will be of the form p/q

The possible roots of f(x) 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.