SOLUTION: Find the linear factorization from the given zeros Zeros: -1, multiplicity 1; 2, multiplicity 3; 4, multiplicity 2

Question 75456: Find the linear factorization from the given zeros
Zeros: -1, multiplicity 1; 2, multiplicity 3; 4, multiplicity 2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
If we are given a zero of any value (say x=a) then the factor will be
. The reason why is if we solved for x we get
. If we have 2 zeros of x=a and x=b, then the factors are
See the pattern?
Simply if we are given zeros, we can easily find the polynomial. So the factors of the polynomial are

Since the 2nd factor has a multiplicity of 3, we cube the 2nd term. Also, since the 3rd term has a multiplicity of 2, we simply square the term

And there's the linear factorization. If you multiplied all the terms out, you would get a polynomial with the same zeros as given in the problem.
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