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