6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a.

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Presentation transcript:

6.5 Day 1 Rational Zeros Theorem

If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a factor of and q must be a factor of

Tominaga Version p is a factor of the constant, q is a factor of the leading coefficient. The list of all p/q is the list of all POSSIBLE RATIONAL ROOTS.

Example: Find all the possible rational zeros for the function.

Testing using synthetic division to find a zero Find all of the p’s Find all of the q’s Make a list of p/q Use synthetic division to determine if the number tested is a zero (if you get 0 for a remainder, you have a root)

Find all rational zeros for the function.

Find all zeros for the function.

Homework 1/30: #7 pg all