Question

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 – 6x8 + x3 – 4x + 3?

Answer 1

 The possible potential root of 5x^{11} – 6x^8  + x^3 – 4x + 3 are

 p's possible values are 1 and 3
 q's possible values are 1 3 5 and 15
hope it helps

Answer 2

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

(+/-)$\frac{1}{15}$,(+/-)$\frac{1}{5}$,(+/-)$\frac{1}{3}$,(+/-)$\frac{3}{5}$,(+/-)$1$,(+/-)$3$