Question

What is the Multiplicity of the Zero x = -3 in the function P(x) = (x - 3)^2(x + 3)?

A) 1
B) 2
C) 3
D) 4

Answer 1

The multiplicity of the zero x = -3 in the function (x - 3)^2(x + 3) is 1, because the factor (x + 3) appears only once and is raised to the first power.

Step-by-step explanation:

The multiplicity of a zero refers to the number of times that zero appears as a root of a polynomial equation.

For the function P(x) = (x - 3)^2(x + 3), we see that x = -3 is a zero of the function.

To find the multiplicity of this zero, we look at the factor which has a root of -3, in this case, it is (x + 3).

Since the factor (x + 3) appears only once and is raised to the first power, the zero x = -3 occurs only once.

Therefore, its multiplicity is 1.