1. ## Rational Root Theorem

I have no idea how to do this could you please provide the steps to solving?

use the rational root theorem to list the possible roots and actual roots
x^4-2x^3-4x^2+11x-6

2. $x= \pm~\frac{p}{q}$

p ia an interger factor of the constant term

q is an interger factor of the leading coefficient

$x^4-2x^3-4x^2+11x-6$

so p is 6 and q is 1

so now factor out 6 and 1

Factors of 6 are $1,2,3,6$

so $\pm~\frac{1,2,3,6}{1}$

so your possible roots are $1,-1,2,-2,3,-3,6,-6$

Now use syntheic division aand try out your roots.

1 and 2 works out nicely

$(x-2)(x-1)(x^2+x-3)$