Given the binomials (x - 3), (x - 1), (x + 2), and (x + 3), which one is a factor of f(x) = 2x3 + 3x2 - 2x - 3?

Question

anonymous · Answer

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myininaya · Answer

So if x-n is a factor of f then x=n is a zero of f.
OR!
If x+n is a factor of f then x=-n is a zero f.

myininaya · Answer

If x-3 is a factor of f then x=3 is a zero of f.
If x-1 is a factor of f then x=1 is a zero of f.
If x+2 is a factor of f then x=-2 is a zero of f.
If x+3 is a factor of f then x=-3 is a zero of f.
Just plug in 3,1,-2,-3 and see which one gives you output zero.

myininaya · Answer

I will give you a hint to save you some work:
-2 is definitely not a zero because it is not in the set of possible rational zeros. 
The possible rational zeros are {factors of your constant, factors of your constant/over the coefficient of the term with high exponent} which does not include -2.