Question

List all possible rational zeros for each polynomial function showing steps: 1) p(x)=3x^3-2x^2-5x-2
2)r(x)=12x^3-17x^2-27x

Answer 1

don't you need to rational zeros theorem

for p(x) the constant is -2 (call it p) so can have factors -1 x 2 or 1 x -2
the leading coefficient is 3 (call it q) so the factors are -1 x -3 or 1 x 3

so the possible rational roots are

\[\frac{p}{q} = \pm \frac{1}{1}, \pm \frac{2}{1}, \pm \frac{1}{3}. \pm \frac{2}{3}\]

and a similar process for r(x)