Answer to Question #342614 in Algebra for Busi

Question

Which of the following is part of the set of all possible rational zeros of

f(x)=2x4−x3+6x2−5x−8?

i.

±1; ±2; ±12; ±14

ii.

±1; ±2; ±4

iii.

±1; ±2; ±4; ±12; ±14

iv.

None of the given options.

v.

±2; ±8; ±14

Answer 1

The trailing coefficient (the coefficient of the constant term) is $-8.$

Find its factors (with the plus sign and the minus sign): $\pm1, \pm2, \pm4, \pm8.$

These are the possible values for $p.$

The leading coefficient (the coefficient of the term with the highest degree) is $2.$

Find its factors (with the plus sign and the minus sign): $\pm1, \pm2.$

These are the possible values for $q.$

Find all possible values of $p/q.$

These are the possible rational roots:

$$\pm \dfrac{1}{2}, \pm1, \pm 2, \pm 4,\pm 8.$$

v.

None of the given options.