Construct a polynomial function with the following properties: fifth degree, −4 is a zero of multiplicity 4, 2 is the only other zero.

is the required polynomial.

Step-by-step explanation:

Multiplicity of the polynomial = 5

⇒The highest power of the variable in the polynomial is 5.

Now, the zero of the polynomial is -4 with multiplicity 4.

⇒ is one the factor of the polynomial.

Also,  the only other zero of the polynomial is 2 with multiplicity 1.

⇒(x-2)  is the ONLY other factor of the polynomial.

Hence, the required polynomial P(x) is

22

step-by-step explanation:

22