Which of the following is a polynomial with roots negative square root of 5, square root of 5, and 3? a. x^3 - 3x^2 - 5x + 15 b. x^3 + 2x^2 - 3x - 6 c. x^3 - 2x^2 - 3x + 6

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 = +/-