we have
\(f(x) = 15x^{11} -6x^{8} + x^{3} - 4x + 3\)
we know that
The Rational Root Theorem states that when a root 'x' is written as a fraction in lowest terms
\(x=\frac{p}{q}\)
p is an integer factor of the constant term, and q is an integer factor of the coefficient of the first monomial.
So
in this problem
the constant term is equal to \(3\)
and the first monomial is equal to \(15x^{11}\) -----> coefficient is \(15\)
So
possible values of p are \(1, and\ 3\)
possible values of q are \(1, 3, 5, and\ 15\)
therefore
the answer is
The all potential rational roots of f(x) are
(+/-)\(\frac{1}{15}\),(+/-)\(\frac{1}{5}\),(+/-)\(\frac{1}{3}\),(+/-)\(\frac{3}{5}\),(+/-)\(1\),(+/-)\(3\)
