Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 3, -2 is the only other zero, leading coefficient is 2.
f(x)=?
can someone ?

Step-by-step explanation:

we know that

2 is a zero of multiplicity 3 of the polynomial

so

we have that

x=2  is a solution of the polynomial

A factor of the polynomial is

----> is elevated to the cube because is a multiplicity 3

and the other solution is x=-2

since the polynomial  is fifth degree, x=-2 must have a multiplicity 2

so

the other factor of the polynomial is  

----> is squared because is a multiplicity 2

therefore

The polynomial is equal to multiply the factors by the leading coefficient

so

is there answer choices?

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b