Answer:
D. 3x-5
Step-by-step explanation:
We have been given an polynomial \(f(x)=3x^3-5x^2-12x+20\) and we are asked to choose the correct option that represents the factor of our given polynomial according to the rational root theorem.
First of all we will factor our polynomial.
\(f(x)=x^2(3x-5)-4(3x-5)\)
\(f(x)=(x^2-4)(3x-5)\)
\(f(x)=(x+2)(x-2)(3x-5)\)
Therefore, (3x-5) will be a factor of our given polynomial and option D is the correct choice.
