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krek1111 [17]
3 years ago
14

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 some help?
Mathematics
1 answer:
Darya [45]3 years ago
5 0

Answer:

f(x)=2(x-2)^{3}(x+2)^{2}

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

(x-2)^{3} ----> 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  

(x+2)^{2} ----> is squared because is a multiplicity 2

therefore

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

so

f(x)=2(x-2)^{3}(x+2)^{2}

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