We are given the following polynomial
[tex]3x^5-7x^4-5x^3+18x^2-5[/tex]
The constant term is -5
The factors of the constant term are ±1 and ±5
The leading coefficient is 3
The factors of the leading coefficient are ±1 and ±3
We can use the factors of the constant term and the leading coefficient to find the potential roots
[tex]potential\; roots=\frac{p}{q}[/tex]
Where p represents the factors of the constant term and q represents factors of the leading coefficient.
[tex]\begin{gathered} \frac{p}{q}=\frac{\pm1,\pm5}{\pm1,\pm3} \\ \frac{p}{q}=\frac{\pm1}{\pm1},\frac{\pm1}{\pm3},\frac{\pm5}{\pm1},\frac{\pm5}{\pm3} \\ \frac{p}{q}=\pm1,\pm\frac{1}{3},\pm5,\pm\frac{5}{3} \end{gathered}[/tex]
Therefore, the potential roots of the given polynomial are
[tex]\pm1,\pm\frac{1}{3},\pm5,\pm\frac{5}{3}[/tex]
