Please help. Having a hard time with this.

Find all of the zeros of the polynomial function and state the multiplicity of each.

f (x) = (x^2 – 16)^2

A. – 4 with multiplicity 2 and 4 with multiplicity 2
B. – 4i with multiplicity 2 and 4i with multiplicity 2
C. 4 with multiplicity 2
D. 4 with multiplicity 4

I say it's A or C but leaning towards A? Any suggestions? Thanks!

(x²-16)²

=(x+4)²(x-4)²

What can you say with the number of distinct zeroes?
What can you say about the multiplicity of each zero?
The order of the polynomial being 4, what can you say about the total number of zeros, all multiplicities taken into account?

If the answer is either A or C, which one would you choose?

I was thinking (A) because of the -16, and we need a - number to get that. Is this right?

A is correct.

There are two distinct roots, so C and D are out of the question.
The zeroes are real, so B is out of the question. That leaves us with A.

To find the zeros of the polynomial function, you need to set the function equal to zero and solve for x.

In this case, the function is f(x) = (x^2 – 16)^2. To find the zeros, you set the function equal to zero:

(x^2 – 16)^2 = 0

To solve this equation, you take the square root of both sides:

√((x^2 – 16)^2) = √0

Simplifying the square root on the left side:

x^2 – 16 = 0

Now, we solve for x by factoring:

(x + 4)(x - 4) = 0

Setting each factor equal to zero:

x + 4 = 0 or x - 4 = 0

Solving for x in each equation:

x = -4 or x = 4

Therefore, the zeros of the polynomial function are x = -4 and x = 4.

Now, let's determine the multiplicities of each zero.

The multiplicity of a zero refers to the number of times the factor (x - zero) appears in the factored form of the polynomial.

Looking at the factored form of the polynomial (x + 4)(x - 4), we can see that (x - 4) appears once and (x + 4) appears once.

Therefore, the multiplicity of -4 is 1 and the multiplicity of 4 is also 1.

So, the correct answer is option C: 4 with multiplicity 2.

Hope this helps!