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

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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) About Me  (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
x-a=0. The reason why is if we solved for x we get
x=a. If we have 2 zeros of x=a and x=b, then the factors are
%28x-a%29%28x-b%29=0 See the pattern?
Simply if we are given zeros, we can easily find the polynomial. So the factors of the polynomial are
%28x%2B1%29%28x-2%29%28x-4%29
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
%28x%2B1%29%28x-2%29%5E3%28x-4%29%5E2
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.