SOLUTION: list all the possible rational zeros of f(x)=3x^3-x^2+2x+2

Question 229700: list all the possible rational zeros of f(x)=3x^3-x^2+2x+2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The rational root theorem says that a constraint on rational solutions (or roots) of the polynomial equation

with integer coefficients is: If

and

are non-zero, then each rational solution

when written as a fraction,

in lowest terms satisfies:

is an integer factor of the constant term

is an integer factor of the leading coefficent

For your problem,

must be an integer factor of 2, so list all of those, and

must be an integer factor of 3, so list those. Remember that 1 is an integer factor of any integer. Now, create all possible fractions of the form

, which is the list of possible rational roots. Remember, not all of the possibles will actually be roots, the theorem only says that IF a rational number is a root, THEN it has that form. The converse of the theorem statement is not necessarily true.

John

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