what are the zeros for (x^2-16)(x^2-4)

Question

I'm wondering how to find the zero's for (x^2-16)(x^2-4). I know zero's are horizontal intercepts, but I can't seem to figure it out. Any help is appreciated. Thank you.

Answer 1

Kate, it looks like the two binomials each have a perfect difference in square in which are

 

(x^2-16)=(x-4)(x+4)

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

 

Hence, the equation becomes,

 

(x-4)(x+4)(x-2)(x+2)

 

Thus, the zeros are the following:

 

x=4, x=-4, x=2, and x=-2.