Tarik Z. answered • 05/26/13

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The rational zeros theorem is a method to determine the possible roots of a function. The rational zeros are p/q, where p are all of the factors of the constant term, and q are all of the factors of the leading coefficient.

For this function, p = +/- 28, +/- 14, +/- 7, +/- 4, +/- 2, +/-1.

And q = +/- 5, +/- 1.

The rational zeros are therefore (all +/-) 28/5, 14/5, 7/5, 4/5, 2/5, 1/5, 28, 14, 7, 4, 2, 1.

Determining that the actual root is in fact 4/5 is tedious and requires applying synthetic division to each of these rational zeros.