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

5th degree means highest power is 5 total

zeroes/roots are

(x-r)

so - 2 is a root

(x - (-2))

(x+2) is a root

multiplicity 2 means it happens 2 times ie

(x+2) ^2

e

4 is the only other zero

(x-4)

so now we have

(x-4) (x+2) ^2

but that is only 3rd degreed

I could add 2 more degrees that are complex roots and therefor won't be graphed on the plane since they are complex so

find a 2nd degree polynomial that has only complex roots

a complex 2nd degree polynomial

x^2+x+10

ok so this is the function

f (x) = (x-4) (x+2) ^2 (x^2+x+10)