Question

Find a polynomial function with the given real zeros whose graph contains the given point. Zeros -2, 0, 2, 1

A) f(x) = (x - 1)(x + 2)(x - 2)(x)
B) f(x) = (x - 1)(x + 2)(x - 2)(x + 2)
C) f(x) = (x + 2)(x - 1)(x + 2)(x - 2)
D) f(x) = (x + 1)(x - 2)(x + 2)(x - 1)

Answer 1

After multiplying (x + 2), (x), (x - 2), and (x - 1) which correspond to the zeros -2, 0, 2, and 1 respectively, the polynomial function that fits the given zeros is Option A: f(x) = (x - 1)(x + 2)(x - 2)(x).

Step-by-step explanation:

To find the polynomial function with the given real zeros of -2, 0, 2, and 1, we must first write down the factors associated with each zero. A zero at x = -2 corresponds to the factor (x + 2), a zero at x = 0 corresponds to the factor (x), a zero at x = 2 corresponds to the factor (x - 2), and a zero at x = 1 corresponds to the factor (x - 1). We then multiply these factors to obtain a polynomial that has these zeros.

The correct polynomial based on the given zeros is:

f(x) = (x + 2)(x)(x - 2)(x - 1)

Looking at the options provided:

• Option A: f(x) = (x - 1)(x + 2)(x - 2)(x) is the correct polynomial function.
• Option B: f(x) = (x - 1)(x + 2)(x - 2)(x + 2) contains a repeated factor and is incorrect.
• Option C: f(x) = (x + 2)(x - 1)(x + 2)(x - 2) also has a repeated factor and is incorrect.
• Option D: f(x) = (x + 1)(x - 2)(x + 2)(x - 1) has incorrect factors and is not the polynomial we are looking for.