For the polynomial below, 1 is a zero of multiplicity two. g(x)=x^4 -6x^3 +38x^2 -62x +29. Express g(x) as a product of linear factors

Question

the answer alone us enough for me.

Answer 1

divide x^4-6x^3 + 38x^2 -62x + 29 by (x-1)^2

= x^2 -4x +29

4x^4 +6x^3 +38x^2 -62x +29

= (x-1)(x-1)(x^2 -4x +29)

use the quadratic formula

x = 4/2 + or - (1/2)sqr(16-116)

x = 2 + or - 10i/2

x = 2+ or -5i

x-2-5i=0

and

x-2+5i =0

g(x) =(x-1)(x-1)x^2-4x +29)

g(x) = (x-1)(x-1)(x-2-5i)(x-2+5i)