Given that −5i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−13x3+65x2−325x+1000

Question

f(x)=

Answer 1

Answer 2

x^4 -13x^3 +65x^2 -325x +1,000 with two zeros -5i and +5i

(x-5i)(x+5i) = x^2+25 divided into the 4th degree polynomial a quadratic =

x^2 -13x +40 which factors into (x-8)(x-5)

the 4D = (x-8)(x-5)(x^2+25) in fully integer factored form