Determine the multiplicity of the roots of the function k (x) = x (x+2) cubed (x+4) squared (x-5) cubed

The degree of the (x - h), whether 1, 2, or 3, says how many multiplicities that linear factor has.

So,

0

-2 (m of 3)

-4 (m of 2)

5 (m of 3)

Multiplicity is the power on the factor.

x (x + 2) ^3 (X + 4) ^2 (x - 5) ^3

x = 0 with multiplicity 1

x = - 2 with multiplicity 3

x = - 4 with multiplicity 2

x = 5 with multiplicity 3