The given function is:
[tex]g(x)=-25x^3-5x^2-2x-1[/tex]
The theorem states that the factors are p/q where p is the factors of the last term (constant term) and q is the factors of the leading coefficient.
Here the leading coefficient is -25 and the constant term is -1.
The factors are listed below:
[tex]\begin{gathered} -25\Rightarrow\pm25,\pm5,\pm1\Rightarrow q \\ -1=\pm1\Rightarrow p \end{gathered}[/tex]
So the value of p/q can be the values shown below:
[tex]\frac{p}{q}\Rightarrow\pm\frac{1}{25},\pm\frac{1}{5},\pm1[/tex]
Hence the possible zeroes of the given function are:
[tex]\pm\frac{1}{25},\pm\frac{1}{5},\pm1[/tex]
