Question 202698: Which one is not a possible rational zero of f(x)=5x^3+3x^2+2? -5/2,2,2/5,or -1/5?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! In general, the possible rational roots of a polynomial are all possible combinations of factors of the constant term (the term without a variable) over factors of the leading coefficient (the coefficient of the term with the highest exponent). Don't forget to include the pairs of negative factors for positive numbers (like in this problem)!
In your polynomial the constant term is 2, whose factors are 1, 2, -1, -2, and the leading coefficient is 5, whose factors are 1, 5, -1, -5. So the possible rational roots are:
1/1 = 1
1/5
1/-1 = -1
1/-5 = -(1/5)
2/1 = 2
2/5
2/-1 = -2
2/-5 = -(2/5)
(Using the negative factors of 2 will just end up repeating the above. If you're not sure about this, go ahead and try them.)
So the only proposed root which is not possible is: -5/2.
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