Question

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

f(x) = 5(x + 8)2(x - 8)3
A. 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3

B. -8, multiplicity 2; 8, multiplicity 3

C. -8, multiplicity 3; 8, multiplicity 2

D. 4, multiplicity 1; 8, multiplicity 1; -8, multiplicity 1

Answer 1

Is that \[f(x) = 5(x+8)^2(x-8)^3\]?

Answer 2

yes

Answer 3

If so, the zeros of the polynomial are found by setting the products = 0. The multiplicity of each zero will just be the power of the product term in the polynomial. For example, if we had the polynomial
\[f(x) = x(x-1)^3(x+2)^2\]
We would have zeros at \(x = 0\), \(x=1\) and \(x=-2\), and the multiplicity would be 1, 3, and 2 respectively.

Answer 4

so it will be A : 4, multiplicity 1; -8, multiplicity 3; 8, multiplicity 3