Find the polynomial fx of degree 7 such that both 2 and 2 ar

Find the polynomial f(x) of degree 7 such that both 2 and -2 are zeros of multiply 2 ,0 is a zero of multiplicity 3 ,and f(-1) = -36

polynomial f(x) of degree 7 such that both 2 and -2 are zeros of multiply 2 ,0 is a zero of multiplicity 3 ,and f(-1) = -36

-----> 2 and -2 are zeros of multiply 2 : ( x-2)^2(x+2)^2

------> 0 is a zero of multiplicity 3 : x^3( x-2)^2(x+2)^2

Let f(x) = kx^3( x-2)^2(x+2)^2

Given : f(-1) = -36

So, -36 = k(-1)(-3)^2(1)^2

-36 = -k*9

k = 4

So, f(x) = 4x^3( x-2)^2(x+2)^2