Question

Which statement accurately describes the roots of the polynomial function f(x) = (x - 3)^4(x + 6)^2?

A - -3 with a multiplicity 2 and 6 with a multiplicity 4
B - -3 with a multiplicity 4 and 6 with a multiplicity 2
C - 3 with a multiplicity 2 and -6 with a multiplicity 4
D - 3 with a multiplicity 4 and -6 with a multiplicity 2

Answer 1

The polynomial function has roots at x = 3 with a multiplicity of 4 and x = -6 with a multiplicity of 2.

Step-by-step explanation:

The polynomial function f(x) = (x - 3)^4(x + 6)^2 can be factored into (x - 3)(x - 3)(x - 3)(x - 3)(x + 6)(x + 6).

By looking at the factors, we can see that the function has roots at x = 3 with a multiplicity of 4 and x = -6 with a multiplicity of 2.

Therefore, the correct statement is option D - 3 with a multiplicity 4 and -6 with a multiplicity 2.