Question

Two is a zero of the equation x³ - x² - 14x + 24 = 0. Which factored form is equivalent to the equation?

1) (x - 3)(x²)(x + 4) = 0
2) (x - 2)(x²)(x + 4) = 0
3) (x - 3)(x - 2)(x + 4) = 0
4) (x⁴)(x - 2√)(x + 2√) = 0

Answer 1

The factored form of the equation x³ - x² - 14x + 24 = 0 that is equivalent is (x - 3)(x - 2)(x + 4) = 0.

Step-by-step explanation:

The factored form of the equation x³ - x² - 14x + 24 = 0 that is equivalent is option 3) (x - 3)(x - 2)(x + 4) = 0.

To determine the factored form, we use the fact that two is a zero of the equation. We can then set up the equation (x - 2) = 0 and solve for x, which gives us x = 2. This means that (x - 2) is a factor of the equation. Now we can use polynomial long division or synthetic division to divide the original equation by (x - 2) to obtain a quadratic equation. Solving that quadratic equation gives us the remaining factors.

Therefore, the factored form of the equation is (x - 2)(x - 3)(x + 4) = 0.