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 [tex] \frac{p}{q} [/tex] these will be the possible rational zeros of the polynomial function:
±([tex] \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} [/tex])
these can be reduced to the following list:
±(1,[tex] \frac{1}{3} [/tex], 2, [tex] \frac{2}{3} [/tex], 3, 4, [tex] \frac{4}{3} [/tex], 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.
