Answer:
[tex]$ x^3 - 5x^2 - 9x + 45 $[/tex]
Step-by-step explanation:
Given the zeroes (roots) of a polynomial are: - 3, 3, 5.
An [tex]$ n - degree $[/tex] polynomial has [tex]$ n - roots $[/tex] (zeroes). The converse is also true.
Also, (x - a) is a factor of the polynomial if and only if x = a is a root of the polynomial.
Here, we are given three roots of the polynomial. That means, the polynomial must be of third degree.
Here the roots are: -3, 3, 5. So, the factors are: (x + 3)(x - 3)(x - 5).
Multiplying them we get the polynomial:
[tex]$ (x + 3)(x - 3)(x - 5) $[/tex]
[tex]$ \implies (x^2 - 9)(x - 5) $[/tex]
[tex]$ \implies x^3 - 5x^2 - 9x + 45 $[/tex] is the required answer.
