We have to determine the complete factored form of the given polynomial
\(f(x)=6x^3-13x^2-4x+15\).
Let x= -1 in the given polynomial.
So, \(f(-1)= 6(-1)^3-13(-1)^2-4(-1)+15 = -6-13+4+15 = 0\)
So, by factor theorem
(x+1) is a factor of the given polynomial.
So, dividing the given polynomial by (x+1), we get quotient as \(6x^2-19x+15\).
So, \(6x^3-13x^2-4x+15\) = (x+1)\(6x^2-19x+15\).
= \((x+1)(6x^2-10x-9x+15)\)
=\((x+1)[ 2x(3x-5)-3(3x-5)]\)
= \((x+1)(2x-3)(3x-5)\) is the completely factored form of the given polynomial.
Option D is the correct answer.
