The given expression 2x^3 + 3x^2 - 11x - 50 can be factored as (2x + 3)(x + 1)(x - 1) using the factor by grouping method.
To factorize the expression 2x^3 + 3x^2 - 11x - 50, we can use synthetic division or factor by grouping. Let's use factor by grouping.
Group the terms in pairs:
(2x^3 + 3x^2) + (-11x - 50)
Now, factor out the common factor from each pair:
x^2(2x + 3) - 1(2x + 3)
Notice that both terms have a common factor of (2x + 3). Factor this out:
(2x + 3)(x^2 - 1)
Now, factor x^2 - 1 further:
(2x + 3)(x + 1)(x - 1)
So, the factorization of 2x^3 + 3x^2 - 11x - 50 is (2x + 3)(x + 1)(x - 1).