R has degree 4 and zeros 2 − 4i and 4, with 4 a zero of multiplicity 2.

Answer 1

They want to construct the polynomial function with those zeros...

(x-4)*(x-4) [( x-2) - 4i][ (x-2) + 4i ]

(x^2 - 8x + 16)[ (x-2)^2 + 16 ]

(x^2 - 8x) +16) ( x^2 - 4x + 20) = P(x)