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.