Question 4(Multiple Choice Worth 1 points) (07.02 MC) Factor completely x^3-2x^2-5x+10 (x-2)(x^2-5) (x+2)(x^2+5) (x-2)(x^2+5) (x+2)(x^2-5)

To factor the polynomial completely, we need to find the roots of the polynomial and express it as a product of linear factors.First, let's use the Rational Root Theorem to identify possible rational roots. The Rational Root Theorem states that any rational root of the polynomial is a factor of the constant term divided by a factor of the leading coefficient .For the polynomial :- The constant term - The leading coefficient The possible rational roots are the factors of 10: .We will test these possible roots by substituting them into the polynomial to see if they yield zero.Let's start with : Next, : Next, : So, is a root. We can now factor out \((x - 2)\) from the polynomial using synthetic division or polynomial division.Using synthetic division to divide by \((x - 2)\): The quotient is , so we have: Thus, the completely factored form of the polynomial is: Therefore, the correct answer is: