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
turksvids
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.

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