P(x)=3x^4-7x^2+12    How do I find all possible rational zeros and then the actual zeros that work?

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The video pretty much explains how to solve it. Just remember to add 0x's as place holders.So your equation could be written as:P(x)=3x^4+0x^3-7x^2+0x+12 (when simplified your gonna get P(x)=3x^4-7x^2+12)and knock yourself out with the synthetic divisions.