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Unformatted text preview: Section 2.5 Zeros of Polynomial Functions Rational Zero Theorem (a.k.a. Possible Rational Roots) for 1 2 2 1 1 ) ( a x a x a x a x a x f n n n n + + + + + = where the coefficients are integers, the possible rational roots of f(x) are of the form , where p is a factor of the constant (a ) and q is a factor of the leading coefficient (a n ). PRR = n a of factors a of factors . = t coefficien leading of factors const of factors .Note : This only gives us rational roots , there could be other irrational ones. EX 1: List all the possible rational zeros of 6 5 2 ) ( 2 3 + = x x x x f EX 2: List all the possible rational zeros of 3 12 4 ) ( 4 5 + = x x x x f .  Now we can use this information to help us find all the roots of a polynomial! 1.) List all possible rational zeros. 2.) Use synthetic division to see if can find a rational zero among all possible rational zeros (when you get a remainder of zero, it is a rational zero) 3.) Rewrite the quotient with the variables and if can solve do so, otherwise repeat the above process...
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This note was uploaded on 11/23/2010 for the course MATH 115 taught by Professor Mcbride,v during the Fall '08 term at University of South Dakota.
 Fall '08
 Mcbride,V
 Integers

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