A polynomial has been factored as #f(x)=(x-6)(x+5)(x-9)#, what are the zeros of the polynomial?

1 Answer
George C.
Jan 4, 2017

#x = 6#, #x = -5# or #x = 9#

Explanation:

#f(x) = (x-6)(x+5)(x-9)#

If all of the linear factors are non-zero, then so is their product #f(x)#.

If any of the linear factors is zero, then so is their product #f(x)#.

So the zeros of #f(x)# are precisely the values of #x# which make at least one of the linear factors #0#, namely: #6#, #-5# or #9#.

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