2. Solving a polynomial equation f(x)=6x^3+25x^2-24x +5

(a) Using the above function, demonstrate use of the Rational Root Test to list (unrepeated) all the potential rational zeros.

(b) Using the above function, demonstrate the following: (i) selecting divisors from the potential rational zeros, (ii) using Remainder Theorem to check whether it is a zero, (iii) whenever it is a zero use synthetic division to find the depressed polynomial, and (iv) repeating until you have the function down to a "solvable" function.

(c) Once you have the function down to a "solvable function", either factor (if possible), use quadratic formula, or square root property to find the remainder of the zeros (real and/or imaginary). Put all solutions in a solution box.