Option D:
f(x) = x(x + 2)(x + 5)
Solution:
Given root of the polynomial functions are:
–5, –2 and 0.
If a is the root of the polynomial then the factor is (x –a).
So that, the factors of the given roots are:
(x –(–5)) = x + 5
(x –(–2)) = x + 2
(x – 0) = x
Polynomial = Product of the factors
f(x) = (x + 5)(x + 2)x
Switch the order of the factors.
f(x) = x(x + 2)(x + 5)
Option D is the correct answer.
The polynomial function of lowest degree is f(x) = x(x + 2)(x + 5).
