Find all zeros of the function (including imaginarys) show all work :

x^3+12x^2+73x+164

  x = -4, -4-5i, -4+5i

Step-by-step explanation:

A graphing calculator shows the one real zero to be at x=-4.

The remaining quadratic can be found by dividing the original polynomial by (x+4), the factor that is zero at x=-4.

That quadratic has vertex form ...

  (x+4)^2 +25

Solving for the zeros, we get ...

  (x+4)^2 +25 = 0

  (x +4)^2 = -25

  x +4 = ±√(-25) = ±5i

  x = -4 ±5i

_____

There are several ways you can find the quadratic factor of this polynomial:

____

* Using a graphing calculator, you need to be careful regarding the vertical scale factor. Here, the leading coefficients of the polynomial and the binomial factor are both 1, so we can use the vertex coordinates directly to find the complex solutions. For a scale factor of 1 and vertex (h, k), the vertex form of the quadratic is (x -h)^2 +k.

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!