Find a polynomial function with the zeros minus11 multiplici

Find a polynomial function with the zeros minus11 (multiplicity 22) and 11 (multiplicity 22), whose graph passes through the point left parenthesis negative 2 comma 45 right parenthesis(2,45).

Solution

Number Text is repeated so i understand Zeros : x= -1( multiplicty 2) ----> (x+1)^2

x = 1( multiplicty 2) ----> (x-1)^2

f(x) = k(x+1)^2(x-1)^2 . Find k using (-2, 45)

So, 45 = k(-2+1)^2(2+1)^2

k = 45/(9) = 5

So, f(x) = 5(x+1)^2(x-1)^2