Question

solve the equation.

\\x^3 - 11x^2 + 30x = 0\\

\\(x = \square\\)
(use a comma to separate answers as needed.)

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Factor out the greatest common factor

$$ x^3 - 11x^2 + 30x = 0 $$

$$ x(x^2 - 11x + 30) = 0 $$

Step 2: Factor the quadratic trinomial

$$ x(x - 5)(x - 6) = 0 $$

Step 3: Solve for x

$$ x = 0 \quad \text{or} \quad x - 5 = 0 \quad \text{or} \quad x - 6 = 0 $$

$$ x = 0, 5, 6 $$

Answer:

0, 5, 6