SOLUTION: Find the zeros of the polynomial​ function, and state the multiplicity of each. f(x)=x^3(x-5)^2(x+9)

Algebra ->  Trigonometry-basics -> SOLUTION: Find the zeros of the polynomial​ function, and state the multiplicity of each. f(x)=x^3(x-5)^2(x+9)      Log On


   

Question 1037195: Find the zeros of the polynomial​ function, and state the multiplicity of each.
f(x)=x^3(x-5)^2(x+9)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3%28x-5%29%5E2%28x%2B9%29 is given in fully factored form.
The zeros are the values of x that make a factor (and hence the product function) zero.
They are:
highlight%28x=0%29 , with multiplicity highlight%283%29 ,
because the factor %28x-0%29=x appears with the exponent 3 in the fully factored expression of f%28x%29 ,
highlight%28x=5%29 , with multiplicity highlight%282%29 ,
because the factor %28x-5%29 appears with the exponent 2 in the fully factored expression of f%28x%29 , and
highlight%28x=-9%29 , with multiplicity highlight%281%29 ,
because the factor %28x-%28-9%29%29=%28x%2B9%29 appears with no exponent
(which is the same having 1 as the exponent)
in the fully factored expression of f%28x%29 .