Question

F(x)=(x+4)(x-2)(x+4)(x+4)

What is the multiple zero? Multiplicity is?

Answer 1

The function F(x) = (x+4)(x-2)(x+4)(x+4) has a multiple zero at x = -4 with a multiplicity of 3. The term x = 2 is a simple zero with a multiplicity of 1.

Step-by-step explanation:

The function F(x) disclosed in the question is F(x) = (x+4)(x-2)(x+4)(x+4).

The multiple zero for this function is x = -4. This is called a multiple zero or a repeated zero because the factor associated with x = -4 appears three times in the function. The multiplicity of this zero is 3, which means the zero is repeated three times in the factorization of the polynomial.

In contrast, x = 2 occurs only once in the factorization, so it is a simple zero with a multiplicity of 1.

Answer 2

`f(x)=(x+4)(x-2)(x+4)(x+4)\\f(x)=(x+4)^3(x-2)=0\\(x+4)^3=0~|~(x-2)=0\\(x+4)(x+4)(x+4)=0~|~x=2\\x=-4,2`

The multiple zero is x = -4.

The multiplicity is 2 because there are two values of x.