Find the zeros of each function. state the multiplicity of any multiple zeros. ( show work) 16. y=3x(x+2)^3 17. y=x^4-8x^2+16

QUESTION 16

The given function is,



To find the zeroes of this function, we equate the function to zero to get,



We now apply the zero product principle to get,



The second factor is repeating 3 times, therefore the root has a multiplicity of 3.

This implies that,


-2 has a multiplicity of 3.

QUESTION 17.

The given expression is





This is now a quadratic equation in x².

We split the middle term to get,



We now factor to obtain,



This implies that,





We apply difference of two squares here to get,



This is the same as,



This time both roots have a multiplicity of 2.

Applying the zero product property, we obtain,



This implies that,



with a multiplicity of 2 each.