Question 3 (2 points) Factor completely 12x^3-40x^2-27x+90 A (4x^2-9)(3x+10) (4x-3)(3x-10)(x+3) (2x-3)(6x^2-11x-30) (2x+3)(2x-3)(3x-10)

To factor the polynomial completely, we can use the Rational Root Theorem to find possible rational roots and then perform polynomial division or synthetic division.First, let's list the possible rational roots. The Rational Root Theorem states that any rational root of the polynomial equation is a fraction , where is a factor of the constant term and is a factor of the leading coefficient .For the polynomial :- The constant term - The leading coefficient Factors of 90: Factors of 12: Possible rational roots are: We will test these possible roots by substituting them into the polynomial to see if they yield zero.Let's start with : Next, let's try : Next, let's try : Next, let's try : Next, let's try : Next, let's try : Next, let's try : Next, let's try : Next, let's try : Next, let's try :\[12(-10)^3 - 40(-10)^2