Question

In the xy-plane, the graph of function f(x) has zeros at −5, −2, and 2. Write the polynomial function.

Answer 1

`f(x) = x^3 +5x^2-4x-20`

Explanation:

Given

`Zeros: -5,-2,2`

Required

The polynomial function

If a function has a, b and c as its zeros, the function is:

`f(x) = (x - a)(x - b)(x - c)`

So, we have:

`Zeros: -5,-2,2`

`f(x) = (x - (-5))(x - (-2))(x - 2)`

Open the inner brackets

`f(x) = (x +5)(x +2)(x - 2)`

Expand the difference of two squares

`f(x) = (x +5)(x^2 - 4)`

Expand

`f(x) = x^3 +5x^2-4x-20`