Question

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

Answer 1

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 $\frac{p}{q}$ these will be the possible rational zeros of the polynomial function:
±($\frac{1}{1} , \frac{1}{3} , \frac{2}{1} , \frac{2}{3} , \frac{3}{1} , \frac{3}{3}, \frac{4}{1} , \frac{4}{3} , \frac{6}{1} , \frac{6}{3} , \frac{12}{1} , \frac{12}{3}$)

these can be reduced to the following list:
±(1,$\frac{1}{3}$, 2, $\frac{2}{3}$, 3, 4, $\frac{4}{3}$, 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.