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

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

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* 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.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

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step-by-step explanation:

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