In the equation f(x) = (3x + 5) (x2 - 6x + 9)2 = 0, 3 has a multiplicity of

Multiplicity is how many times the root (or zero) is repeated

example, in the root b has a multiplicity of n and the root d has a multiplicity of m

first we need to get the roots into
for (3x+5), we need to force factor out the 3 to get


factor the other one

but it is which is equivilent to which simplifies to

so we get

so the roots are -5/3 multiplicity 1 and 3 multiplicity 4

3 has a multilicity of 4