Question

What are all the potential rational roots of f(x)=15x^11 -6x^8 +x^3-4x+3

Answer 1

The theorem of rational solutions states that, given a polynomial with integer coefficients, every potenial rational solution is written as $\frac{p}{q}$, where $p$ divides the constant term, and $q$ divides the leading term.

So, our choices for $p$ are $\pm 1, \pm 3$, while our choices for $q$ are $\pm 1, \pm 3, \pm 5, \pm 15$.

Combine all possible numerator and denominator to get all the potenial rational solutions:

$\pm\frac{1}{1},\pm\frac{1}{3},\pm\frac{1}{5},\pm\frac{1}{15}$

$\pm\frac{3}{1},\pm\frac{3}{3},\pm\frac{3}{5},\pm\frac{3}{15}$