Solve the inequality. (Enter your answer using interval notation.)

2*x*3 + 9*x*2 − 18*x* ≥ 81

We are given the inequality:

\[
2x^3 + 9x^2 - 18x \geq 81
\]

### Step 1: Move all terms to one side.
Subtract 81 from both sides to set the inequality to zero:

\[
2x^3 + 9x^2 - 18x - 81 \geq 0
\]

### Step 2: Factor the inequality.
Let's start by factoring the polynomial. First, notice that we can factor out a 2 from all the terms:

\[
2(x^3 + \frac{9}{2}x^2 - 9x - 40.5) = 0

Solve the inequality. (Enter your answer using interval notation.) 2*x^3 + 9*x^2 − 18*x ≥ 81

Discover how to solve the polynomial inequality 2x^3 + 9x^2 - 18x ≥ 81 using factorization and the zero product property. This solution is ideal for students in Grades 10-12 and covers key algebraic concepts, including cubic functions and polynomial inequalities.

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