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
`(p)/(q)` these will be the possible rational zeros of the polynomial function:
±(
`(1)/(1) , (1)/(3) , (2)/(1) , (2)/(3) , (3)/(1) , (3)/(3), (4)/(1) , (4)/(3) , (6)/(1) , (6)/(3) , (12)/(1) , (12)/(3)`)

these can be reduced to the following list:
±(1,
`(1)/(3)`, 2,
`(2)/(3)`, 3, 4,
`(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.