Question

Consider polynomial function f f(x)=(x-1)²(x+3)³(x+1)use the equation to complete each statement about this function

The zero located and x=1 has a multiplicity of __ and the zero located at x=-3 has a multiplicity of __. The graph of the function will touch, but not cross, the x-axis at the x-value of __.

Answer 1

The polynomial function f(x) = (x-1)²(x+3)³(x+1) has a zero with a multiplicity of 2 at x=1 and a zero with a multiplicity of 3 at x=-3. The graph of the function will touch, but not cross, the x-axis at x=-1.

Step-by-step explanation:

The polynomial function f(x) = (x-1)²(x+3)³(x+1) has zeros located at x = 1 and x = -3. The multiplicity of the zero located at x = 1 is 2 because the factor (x-1)² appears twice in the function. The multiplicity of the zero located at x = -3 is 3 because the factor (x+3)³ appears three times.

The graph of the function will touch, but not cross, the x-axis at the x-value of x = -1. This is because the factor (x+1) does not have a squared term, indicating that the graph will touch the x-axis but not cross it at this point.