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

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0