Given that −8i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable.

Question

f (x) = x^4 + 8x^3 + 79x^2 + 512x + 960

Answer 1

If x=c is a root, then (x - c) is a factor of f(x).  So you will divide f(x) by (x - c).  Since your root is complex, the conjugate of the given root will be your second root.  In other words, your factor will be quadratic.

 

When you divide f(x), which is a 4th degree function, by a quadratic factor, your quotient will be a quadratic.  Then, you will be able to factor it using FOIL or the quadratic formula.