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
`(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(1)/(1),\pm(1)/(3),\pm(1)/(5),\pm(1)/(15)`

`\pm(3)/(1),\pm(3)/(3),\pm(3)/(5),\pm(3)/(15)`