Finding roots of a polynomial of a high degree

[iduque]

Find all roots of the function F(x) = 3x^5 + 2x^4 - 25x^3 - 28x^2 + 12

I know when it comes to these type of problems, you're supposed to look for a pattern and substitute another variable but I don't see another variable and factoring out an x doesn't help either.

How do I go about this?

 

[stapel]

Find all roots of the function F(x) = 3x^5 + 2x^4 - 25x^3 - 28x^2 + 12

I know when it comes to these type of problems, you're supposed to look for a pattern and substitute another variable but I don't see another variable and factoring out an x doesn't help either.

How do I go about this?

I have no idea what "method" you're talking about...? To learn a standard method for solving polynomials (that is, for setting them equal to zero and finding all of the solutions, which are the roots), try here.

The first step (which you don't show in your hand-in solution) is graphing, so you can make more intelligent "guesses" from the list provided by the Rational Roots Test. This step is quite the time-saver on tests.