We have to determine the complete factored form of the given polynomial
[tex]f(x)=6x^3-13x^2-4x+15[/tex].
Let x= -1 in the given polynomial.
So, [tex]f(-1)= 6(-1)^3-13(-1)^2-4(-1)+15 = -6-13+4+15 = 0[/tex]
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 [tex]6x^2-19x+15[/tex].
So, [tex]6x^3-13x^2-4x+15[/tex] = (x+1)[tex]6x^2-19x+15[/tex].
= [tex](x+1)(6x^2-10x-9x+15)[/tex]
=[tex](x+1)[ 2x(3x-5)-3(3x-5)][/tex]
= [tex](x+1)(2x-3)(3x-5)[/tex] is the completely factored form of the given polynomial.
Option D is the correct answer.
