Question

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

Answer 1

ANSWER

All the potential rational zeros are:


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

Step-by-step 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`