The correct answer is A) x^3 - 3x^2 - 5x + 15
In order to solve this, we start by factoring using a method called splitting. To do so, we only look at the front two terms to start and take out the greatest common factor.
x^3 - 3x^2
x^2(x - 3)
Now we do the same for the second half (the last two terms).
-5x + 15
-5(x - 3)
Since the left over parenthesis is the same in both cases, we can use that along with the greatest common factors in a set of parenthesis, which is the factored form.
(x^2 - 5)(x - 3)
Now to find the root, we set each of these equal to 0.
x - 3 = 0
x = 3
x^2 - 5 = 0
x^2 = 5
x = +/-[tex]\sqrt{5}[/tex]
