Answer:
[tex]f (x) = x (x + 5) (x-9)[/tex]
Step-by-step explanation:
The zeros of the polynomial are all the values of x for which the function [tex]f (x) = 0[/tex]
In this case we know that the zeros are:
[tex]x = 9,\ x-9 =0[/tex]
[tex]x = 0[/tex]
[tex]x = -5[/tex], [tex]x + 5 = 0[/tex]
Now we can write the polynomial as a product of its factors
[tex]f (x) = x (x + 5) (x-9)[/tex]
Note that the polynomial is of degree 3 because the greatest exponent of the variable x that results from multiplying the factors of f (x) is 3
