List possible rational zeroes of the function. 3x^5-8x^4+6x^2+7x-12.

First list all the positive and negative factors of the constant term in the expression: ±(1,2,3,4,6,12) these will be the values for "p"

Second list all the positive and negative factors of the leading coefficient:
±(1,3) these will be the values for "q"

Now list all the possible values of these will be the possible rational zeros of the polynomial function:
±()

these can be reduced to the following list:
±(1,, 2, , 3, 4, , 6, 12

This list represents the possible rational zeros of the function. You can then use synthetic division to narrow down the actual roots of the function.

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