Answer:
[tex]a(x+3)^3, a \neq 0[/tex]
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.
Zero at x= -3 with a multiplicity of 3.
This means that:
[tex]x_1 = x_2 = x_3 = -3[/tex]
So
[tex]a(x - (-3))*(x - (-3))*(x-(-3)) = a(x+3)(x+3)(x+3) = a(x+3)^3[/tex]
Positive leading coefficient
[tex]a(x+3)^3, a \neq 0[/tex]
