Find all
the rational zeros of the function p(x)=x^{4}+2x^{3}-14x^{2}+2x-15
(order from least to greatest)

x= ,

The possible rational zeros (by the Rational Zero Test) are as follows:

x=±3, ±5, ±1, ±15

Take a look at the graph of this function to see which x values you can rule out and test the x values that make sense using synthetic division:

Looking at this graph, we know that the only rational zeros that are possible are x=-5 and x=3.

The
complete factorization of x^{4}+2x^{3}-14x^{2}+2x-15=
(x+5)(x-3)(x^{2}+1)

[note: the
solutions to x^{2}+1 are not real, therefore are not included in the
“rational zeros” of this function]