Is this correct?

Using Rational Roots Theorem, list all possible rational root of f(x) = 2x^3 - 3x^2 + 5x+6
Possible roots are p/a = -+1, -+2, +-3, -+6. -+3/2

Yes!

Yes, that is correct! In order to find the possible rational roots of a polynomial function, we can use the Rational Roots Theorem.

The Rational Roots Theorem states that if a polynomial function has a rational root p/q, where p is a factor of the constant term and q is a factor of the leading coefficient, then p/q is a possible rational root.

For the given polynomial function f(x) = 2x^3 - 3x^2 + 5x + 6, the constant term is 6 and the leading coefficient is 2.

To list all possible rational roots using the Rational Roots Theorem, we first find all the factors of the constant term (6) and the leading coefficient (2). The factors of 6 are +/- 1, +/- 2, +/- 3, and +/- 6. The factors of 2 are +/- 1 and +/- 2.

Now, we can form all possible combinations of the factors:
Possible roots are p/q = +/- 1/1, +/- 2/1, +/- 3/1, +/- 6/1, +/- 1/2, and +/- 3/2.

So, the possible rational roots of f(x) = 2x^3 - 3x^2 + 5x + 6 are p/q = +/- 1, +/- 2, +/- 3, +/- 6, +/- 1/2, and +/- 3/2.