f (x)= (x^4+2x^3-17x^2-18*x+72)/(x^3-13x-12), find the x-intercept(s)?

Answer 1

Since you want to find the x-intercepts, you equate f(x) = 0. So now, the denominator is not important.

Use factor theorem. Try x=2, thus one factor is (x-2).
f(x) = (x-2)(x^3+ 4x^2 - 9x -36)
= ...
= (x-2)(x-3)(x+3)(x+4)

You get the drill. Happy solving!

Answer 2

I can´t read the denominator but in any case you must verify that
a root of the numerator is NOT a root of the denominator.
In this case that number is not a solution