math help!! really hard Pre-calc?

If your polynomial equation is of the form

.. a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0 = 0

where a_k are all rational numbers, the rational root theorem tells you any rational roots will be factors of

.. (a_0)/(a_n)

You can use this theorem to limit the scope of trial-and-error testing you do to find the rational roots of the equation.

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Other theorems can provide additional assistance to reduce the scope of trial-and-error testing. Descarte's rule of signs can tell you to quit looking for more roots of a particular sign after you have found as many as there are. See the source link for additional information on the bounds on positive roots. (Realize that when you change the signs of the coefficients of odd powers, you change the signs of the roots from negative to positive.)

The rational root test applies to a polynomial with integer coefficients. If you have rational coefficients, multiply by the least common denominator, and you get a polynomial with integer coefficients. Then you can apply the RRT by looking at the high order coefficient and the constant in the usual way.

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