Construct a polynomial function with the following properties: fifth degree, 3 is a zero of multiplicity 3, −2 is the only other zero, leading coefficient is 2.

2(x - 3)^3(x + 2)^2.

Step-by-step explanation:

 The zero 3 and multiplicity 3 means the factor

(x -3)^3 is included.

The only other zero is -2  which gives us (x + 2)^2,  - it must be multiplicity 2 because the equation is of the fifth degree so there must be 5 zeroes.

The leading coefficient is 2  so our function is:

2(x - 3)^3(x + 2)^2.