Why is it important to consider multiplicity when determining the roots of a polynomial equation?

It is important to consider multiplicity of root in factorization of polynomial equations.

Step-by-step explanation:

We define multiplicity as:

The multiplicity of a root of a polynomial equation is the number of times it appears in the solution. For example, the number of times a given polynomial equation has a root at a given point is the multiplicity of that root.Thus, if we do not consider the multiplicity of a root we may consider the discrete root only and not the number of times the root repeats itself and end up calculating wrong roots for the polynomial equation.Multiplicity tells us that how many times does a factor repeats itself in the factorization of a polynomial.If  r  is a zero of a polynomial and it repeats itself k times in the factorization then we say that  r has multiplicity  k. Zeroes with a multiplicity of 1 are often called simple zeroes.

Thus, it is important to consider multiplicity of root in factorization of polynomial equations.

I’m not absolutely sure but i think it’s 7x6x5x4x3x2=5040 because as the first character you can take any of the 7 given then you are left with 5 then 6 then 4 etc.