Question

Three is a zero of the equation x³ - 4x² - 3x + 18 = 0. Which factored form is equivalent to the equation?

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

Answer 1

The factored form that is equivalent to the equation x³ - 4x² - 3x + 18 = 0 is (x - 2)(x - 3)(x + 3) = 0.

Step-by-step explanation:

The factored form that is equivalent to the equation x³ - 4x² - 3x + 18 = 0 is (x - 2)(x - 3)(x + 3) = 0.

To find the factored form, we use the zero property of equations which states that if a number is a root of an equation, then (x - a) is a factor of the equation, where a is the root.

In this case, since 3 is a zero of the equation, we have (x - 3) as a factor. Using long division or synthetic division, we can find that the quotient is x² - x - 6. Using factoring or the quadratic formula, we can further factor the quotient to (x - 2)(x + 3). Therefore, the factored form equivalent to the equation is (x - 2)(x - 3)(x + 3) = 0.