For the polynomial below list each real zero and its multiplicity f(x)=3(x+6)(x+5)4. Please show all your work.Need correct answer.

1 Answer

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nathanshields | High School Teacher | (Level 1) Associate Educator

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If f(x) = 0 then


So basically you have some stuff multiplied together to make 0.  This means that one of the things you multiply must be 0.

The 3 is not 0.  The (x+6) might be 0.  The (x+5) might be 0.

So x = -6 or -5. These are the roots of the function.

The multiplicity is how many times each root occurs in the factorization of the function.  So since

`f(x)=3(x+6)(x+5)(x+5)(x+5)(x+5)` ,

The roots are x = -6 (mutiplicity 1), and x = -5 (multiplicity 4)