The given polynomial is: $p(x) = 2x^3 - 5x^2 + x + 2$

To find all the zeros of this polynomial, we'll use the Rational Root Theorem, synthetic division, and factoring if possible.

Step 1: Apply the Rational Root Theorem

The Rational Root Theorem suggests that possible rational roots of the polynomial are of the form: $\pm \frac{\text{factors of the constant term}}{\text{factors of the leading coefficient}}$

For $p(x) = 2x^3 - 5x^2 + x + 2$:

• The constant term is $2$, with factors $\pm 1, \pm 2$.
• The leading coefficient is $2$, with factors $\pm 1, \pm 2$.

The possible rational roots are: $\pm 1, \pm 2, \pm \frac{1}{2}$

Step 2: Test the possible roots using synthetic division

Let's start by testing