Question

Find the fourth-degree polynomial function with zeros 2, -2, 2i, and -2i. Write the function in factored form.

Answer 1

To find the fourth-degree polynomial function with given zeros, use the fact that zeros correspond to factors of the polynomial. The fourth-degree polynomial function: f(x) = (x - 2)(x + 2)(x - 2i)(x + 2i)

Step-by-step explanation:

To find the fourth-degree polynomial function with zeros 2, -2, 2i, and -2i, we use the fact that zeros of a polynomial correspond to its factors. In this case, the zeros are 2, -2, 2i, and -2i, so the factors are (x - 2), (x + 2), (x - 2i), and (x + 2i). Since complex zeros always come in conjugate pairs, we can simplify the factors to (x - 2)(x + 2)(x - 2i)(x + 2i). Multiplying these factors together, we get the fourth-degree polynomial function:

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

Answer 2

`f(x) = {x}^(4) - 16`

Step-by-step explanation:

`f(x) = (x + 2i)(x - 2i)(x - 2)(x + 2)`

`f(x) = ( {x}^(2) + 4)( {x}^(2) - 4)`

`f(x) = {x}^(4) - 16`