Final answer:
To solve the inequality 2x^3 - x^2 + 4x - 21 ≥ 0, we can factor the expression and solve the resulting equations.
Step-by-step explanation:
To solve the inequality 2x^3 - x^2 + 4x - 21 ≥ 0, we can use a graphing method or factoring method.
Using the factoring method, we can factor the expression to (x-3)(2x^2+5x+7) = 0. This gives us two possible solutions: x = 3 and the quadratic expression 2x^2 + 5x + 7 = 0. Solving the quadratic equation gives us two more solutions.
Putting all the solutions together, we can write the solution in interval notation as x ≤ 3 and (approximately) x ≤ -3.14 or x ≥ 0.48.