Question

Solve and factor the quadratic equation n³ - 9n = 0.

a. n = 0
b. n = 3
c. n = -3
d. n = ±3

Answer 1

To factor the equation n³ - 9n = 0, we start by factoring out n and then use the difference of squares to factor further, giving us the solutions n = 0, n = 3, and n = -3.

Step-by-step explanation:

To solve and factor the quadratic equation n³ - 9n = 0, we start by factoring out the common factor of n, which gives us:

n(n² - 9) = 0.

Next, we recognize that n² - 9 is a difference of squares and can be factored further into:

n(n + 3)(n - 3) = 0.

Now we set each factor equal to zero:

• n = 0
• n + 3 = 0, which gives n = -3
• n - 3 = 0, which gives n = 3

Thus, the solutions to the equation are:

n = 0, n = 3, and n = -3.

These solutions correspond to the choices a, b, and c.