The degree of the polynomial function h(x) is 10.
The degree of a polynomial function is determined by the highest power of the variable in the polynomial. In this case, the given polynomial function h(x) has real x-intercepts of -5, -1, 4, and 10, with each having a multiplicity of one.
From the table, we can see that the x-intercepts are represented by the values of x where h(x) is equal to zero.
Therefore, the degree of h(x) is equal to the highest power of x in the list of x-intercepts, which is 10. Hence, the degree of h(x) is 10.
The probable question may be:
A polynomial function h(x) has a zero of x=3-4i with a multiplicity of one. Certain values of h(x) are given in the following table. \table[[x,h(x)],[-5,0],[-2,3],[-1,0],[1,2],[4,0],[7,6],[10,0]] If every real x-intercept of h(x) is shown in the table and each has a multiplicity of one, what is the degree of h(x) ?