Find the roots of x3 - 2x2 - 5x + 6 = 0

To find the roots of the given equation, we can use the factoring method or the Rational Root Theorem. Factoring is a bit tedious, so let's use the Rational Root Theorem instead. The Rational Root Theorem states that if a polynomial equation with integer coefficients has any rational roots, then they must be of the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient. For the given equation, the leading coefficient is 1, and the constant term is 6. So the possible rational roots are ±1, ±2, ±3, ±6. We can try each of these values one by one and see if it satisfies the equation. After trying out each value, we find that x=1 is a root of the equation. Now that we have found one root, we can divide the polynomial equation by (x-1) to get a quadratic equation. We can then factor this quadratic equation or use the quadratic formula to find the remaining roots. Dividing the equation by (x-1), we get: x^2 - x - 6 = 0 This quadratic equation factors as (x-3)(x+2) = 0. Therefore, the roots of the original equation are 1, -2, and 3. So the answer is: The roots of x^3 - 2x^2 - 5x + 6 = 0 are 1, -2, and 3.