Answer: p(x) = -n*(x - 3)^2*(x + 2)*(x + 3)
Step-by-step explanation:
For a polynomial whit roots a, b, c, d, e, ... (Where those numbers are not necessarly different)
We can write a polynomial with those roots as:
A*(x -a)*(x - b)*(x - c)*....
Where A is a real number, and it's the leading coefficient (The coefficient that multiplies the highest power term)
In this case we have the roots:
3, 3, -2 and -3 (3 is two times, because it has a multiplicity of 2)
Then this polynomial can be written as:
A*(x - 3)*(x - 3)*(x + 2)*(x + 3)
And we know that the leading coefficient is negative, then we can write:
A = -n, where n > 0.
Then our polynomial is:
p(x) = -n*(x - 3)^2*(x + 2)*(x + 3)
