R has degree 4 and zeros 5 − 2i and 4, with 4 a zero of multiplicity 2.

Answer 1

x^4-8x^3-13x^2 +232x - 464 = 0

(x^2-29)(x-4)^2

(x-4) is the factor with zero = 4

(x-4)^2 gives it multiplicity 2

(x^2-29) = (x-(5-2i)(x+(5-2i) = x^2 - (5-2i)^ = x^2 - (25 - (2i)^2 = x^2 - 25 -(-4(-1) = x^2 - 29

just change the sign of the zero and add it to x to get the corresponding factor

the missing zero is the conjugate of the imaginary zero