Help finding multiplicity and zeros?

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The discussion focuses on finding the multiplicities and zeros of the polynomial expression (x+4)(x-2)^3(x^2+2x-8). The correct multiplicities identified are -4 for the zero at x = -4 and 4 for the zero at x = 2. The quadratic factor (x^2 + 2x - 8) simplifies to (x-2)(x+4), confirming that the complete factorization is (x+4)^2(x-2)^4.

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(x+4) (x-2)^3 (x^2+2x-8)

would it be -4 multiplicity of 2
and 2 multiplicity of 4?
 
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Yes, that's correct since the quadratic factor is the product of the other two linear factors.
 
in other words,
(x+ 4)(x- 2)^3(x^2- 2x- 8)= (x+ 4)(x- 2)^3(x- 2)(x+ 4)= (x+ 4)^2(x- 2)^4
as I am sure you realized.
 

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