Question

which of the following represents the polynomial function in factored form that has zeros at x = -1, x = 2, and x = 3?
○ f(x) = (x + 1)(x - 2)(x - 3)
○ f(x) = (x + 1)(x + 2)(x + 3)
● f(x) = (x - 1)(x + 2)(x + 3)
○ f(x) = (x - 1)(x - 2)(x - 3)

Explanation:

Step1: Recall Zero-Factor Theorem

If \( x = a \) is a zero of a polynomial, then \( (x - a) \) is a factor.

Step2: Identify Factors from Zeros

Zeros are \( x = -1 \), \( x = 2 \), \( x = 3 \).

• For \( x = -1 \), factor is \( (x - (-1))=(x + 1) \).
• For \( x = 2 \), factor is \( (x - 2) \).
• For \( x = 3 \), factor is \( (x - 3) \).

Thus, the polynomial in factored form is \( f(x)=(x + 1)(x - 2)(x - 3) \).

Answer:

\( f(x)=(x + 1)(x - 2)(x - 3) \) (the first option among the given choices)