use the rational zeros theorem to list all possible rational zeros for the given function.\n$f(x)=2x^{4}+4x^{…

use the rational zeros theorem to list all possible rational zeros for the given function.\n$f(x)=2x^{4}+4x^{2}-8x + 8$\npossible rational zeros:\nquestion help: message instructor\nnext question

use the rational zeros theorem to list all possible rational zeros for the given function.\n$f(x)=2x^{4}+4x^{2}-8x + 8$\npossible rational zeros:\nquestion help: message instructor\nnext question

Answer

Explanation:

Step1: Identify the constant term and leading coefficient

The constant term ( p = 8 ), and the leading coefficient ( q = 2 ).

Step2: Find the factors of ( p ) and ( q )

Factors of ( p = 8 ): ( \pm1,\pm2,\pm4,\pm8 ) Factors of ( q = 2 ): ( \pm1,\pm2 )

Step3: Calculate possible rational zeros

Possible rational zeros (=\frac{\text{Factors of }p}{\text{Factors of }q}) [ \begin{align*} \frac{\pm1}{\pm1}&=\pm1\ \frac{\pm1}{\pm2}&=\pm\frac{1}{2}\ \frac{\pm2}{\pm1}&=\pm2\ \frac{\pm2}{\pm2}&=\pm1\ \frac{\pm4}{\pm1}&=\pm4\ \frac{\pm4}{\pm2}&=\pm2\ \frac{\pm8}{\pm1}&=\pm8\ \frac{\pm8}{\pm2}&=\pm4 \end{align*} ]

Answer:

(\pm1,\pm\frac{1}{2},\pm2,\pm4,\pm8)