Answer:
The polynomial is [tex]p(x) = ax^3(x+2)^3(x-2)[/tex], in which a is the leading coefficient.
Step-by-step explanation:
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
-2 as a zero of multiplicity 3
This means that:
[tex]p(x) = (x-(-2))^3 = (x+2)^3[/tex]
0 as a zero of multiplicity 3
Then also:
[tex]p(x) = (x+2)^3(x-0)^3 = x^3(x+2)^3[/tex]
2 as a zero of multiplicity 1.
Then:
[tex]p(x) = x^3(x+2)^3(x-2)[/tex]
Adding the leading coefficient:
[tex]p(x) = ax^3(x+2)^3(x-2)[/tex]
The polynomial is [tex]p(x) = ax^3(x+2)^3(x-2)[/tex], in which a is the leading coefficient.
