Question

find the zeros for the polynomial function and give the multiplicity for each zero. state whether the graph crosses the x - axis or touches the x - axis and turns around at each zero. f(x)=x^{3}+4x^{2}-9x - 36. the zeros are - 4, - 3,3. (use a comma to separate answers as needed.) the multiplicity of the greatest zero is 1. (type a whole number.) the multiplicity of the second greatest zero is 1. (type a whole number.) the multiplicity of the smallest zero is 1. (type a whole number.) determine whether the graph crosses the x - axis, or touches the x - axis and turns around at each x - intercept. what is the behavior of the graph at the greatest zero? crosses the x - axis touches the x - axis and turns around

Explanation:

Step1: Recall zero - multiplicity rule

If the multiplicity of a zero of a polynomial is odd, the graph of the polynomial crosses the x - axis at that zero. If the multiplicity is even, the graph touches the x - axis and turns around.

Step2: Analyze given zero multiplicities

The zeros of the polynomial \(f(x)=x^{3}+4x^{2}-9x - 36\) are \(x=-4,x = - 3,x = 3\) and each has a multiplicity of 1 (an odd number).

Answer:

crosses the x - axis