Question

Use the Rational Zeros Theorem to write a list of all potential rational zeros. f(x) = x3 - 5x2 + 8x - 24

Answer 1

If I remember correctly this would be  obtained from the factors of  -24

so i think its +/-1, +/-2, +/- 3, +/- 4, +/- 8, +/- 6 , +/-12, +/-24

Sorry but i cant be sure

Answer 2

ANSWER

All the potential rational zeros are:

$\pm1,\pm2,\pm3,\pm4,\pm6,\pm8,\pm12,\pm24$

EXPLANATION

The given polynomial function is

$f(x) = {x}^{3} - 5 {x}^{2} + 8x - 24$
The leading coefficient is
$1$
The constant term of the polynomial is
$- 24$


According to the rational zeros theorem, the possible rational zeros of the given polynomial are all the factors of -24 expressed over all the factors of 1 in the simplest form.

The possible rational zeros are,

$\pm1,\pm2,\pm3,\pm4,\pm6,\pm8,\pm12,\pm24$