Question

Suppose that the polynomial function f is defined as follows.f(x) = 4(x-9)(x+8)(x - 5)2(x+12) 3List each zero of faccording to its multiplicity in the categories below.If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None."

Answer 1

Given the polynomial:

$f(x)=4(x-9)(x+8)(x-5)^2(x+12)^3$

we can clearly see that the roots of the polynomial are 9, -8, 5 and -12.

Then, notice that the factors (x-9) and (x-8) have exponent 1, therefore, 9 and -8 have multiplicity of 1

Then, (x-5) has exponent 2, this means that the root 5 has multiplicity of 2

Finally, the factor (x+12) has exponent 3, which means that the root -12 has multiplicity of 3