Question

(x-4)^3(x+3)^2

What are the real zeros and the multiplicities of this ??

Answer 1

x = 4 , x = -3

Answer 2

x = 4 , x = -3 is the correct answer.

Answer 3

you are asking about what values make
(x-4)^3(x+3)^2 =0

hopefully it is clear that x=4 would be the expression zero. Or x=-3

Note that we can expand the expression to be
(x-4)(x-4)(x-4)(x+3)(x+3)=0

The root x=4 has a multiplicity of 3, and the root x= -3 has a multiplicity of two