Find all roots of the polynomial \(2x^3 - 3x^2 - 5x + 6\)

Step 1 ：Step 1: Identify the coefficients of the polynomial and list them. The coefficients are 2, -3, -5, and 6.

Step 2 ：Step 2: List the factors of the constant term (6) and the leading coefficient (2). The factors of 6 are \(\pm 1, \pm 2, \pm 3, \pm 6\) and the factors of 2 are \(\pm 1, \pm 2\).

Step 3 ：Step 3: Form the ratio of each factor of the constant term to each factor of the leading coefficient. The potential rational roots are \(\pm 1, \pm 2, \pm 3, \pm 6, \pm \frac{1}{2}, \pm \frac{3}{2}\).

Step 4 ：Step 4: Substitute each potential root into the polynomial until you find one that makes the polynomial equal to zero. After testing, we find that 1, -2 and 3 are roots of the polynomial.

Step 5 ：Step 5: Therefore, the roots of the polynomial \(2x^3 - 3x^2 - 5x + 6\) are 1, -2, and 3.