How many possible positive and negative zeros are in 3x^5 + 6x?

How many possible positive and negative zeros are in 3x^5 + 6x?
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You do not need the rule of signs to determine the number of positive and negative roots. Start by factoring out x to get x(3x^4 + 6) = 0. We have one root at x=0. Let’s check for the solutions of 3x^4 + 6 = 0. Rearranging the terms gives x^4 = -2. This has no real solutions, positive or negative, since any real number raised to an even power must be greater than or equal to 0.
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