Question

What is the multiple zero and multiplicity of f(x)=(x+4)(x-2)(x+4)(x+4)?

Answer 1

A multiple zero is going to generate multiple identical product terms. The multiplicity is simply the number of such terms. Figure out which term(s) are repeated, and how many there are.

Answer 2

Some extra info: if you have a multiplicity which is odd, the zero will be the curve crossing the x-axis. If an even multiplicity, the curve touches the x-axis and then retreats.

http://www.biology.arizona.edu/biomath/tutorials/polynomial/GraphingPolynomials.html