Question #66e6f

1 Answer
Nov 13, 2017

f(x)=3x^3-5x^2-12x+20=(x+2)(x-2)(x-5/3)

Explanation:

The rational root theorem basically tells us what the possible zeroes could be of a polynomial function. To use the rational root theorem, first look at the constant term of the polynomial (call this number p):

f(x)=3x^3-5x^2-12x+color(red)(20)

Then find all the factors of that number:

1, 20, 2, 10, 4, 5 and -1, -20, -2, -10, -4, -5

Next look at the leading coefficient (call this number q):

f(x)=color(red)(3)x^3-5x^2-12x+20

Again find the factors:

1, 3 and -1, -3

Now list all the possible factors of p divided by all the factors of q:

+-1, +-20, +-2, +-10, +-4, +-5, +-1/3, +-20/3, +-2/3, +-10/3, +-4/3, +-5/3

Now you have to try plugging in all these numbers for x to find out which one makes f(x)=0

After a lot of computation, you will find that -2, 2, and 5/3 make f(x)=0, so:

f(x)=3x^3-5x^2-12x+20=(x+2)(x-2)(x-5/3)