Question

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

Answer 1

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)