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 June 10th, 2011, 06:33 AM #1 Newbie   Joined: Jun 2011 Posts: 4 Thanks: 0 Why can't 3/2 be a factor of this polynomial? Why can't be a factor of ? At first I thought it was due to the combination of 3/2 not matching up with the possibilities given by the rational root test. The possible roots given by the test would be . I don't think that the rational root test gives a complete set of possibilities though, so what other reasons could there be a root can be excluded from being a possible root? June 10th, 2011, 06:59 AM #2 Senior Member   Joined: Feb 2010 Posts: 706 Thanks: 141 Re: Why can't 3/2 be a factor of this polynomial? You've got it. The rational roots theorem says that if p/q is a rational root of some polynomial equation with integer coefficients, then p must be a factor of the constant term and q must be a factor of the leading coefficient. 3 is not a factor of 5. June 10th, 2011, 07:12 AM #3 Newbie   Joined: Jun 2011 Posts: 2 Thanks: 0 Re: Why can't 3/2 be a factor of this polynomial? Rational Root Test Suppose we have a polynomial equation where , the coefficients being integers. If and are nonzero, then each rational solution x, when written as a fraction in lowest terms (i.e., the greatest common divisor of p and q is 1), satisfies p is an integer factor of the constant term , and q is an integer factor of the leading coefficient . The given polynomial may or may not have rational solutions. But cannot be a solution since 3 is not an integer factor of the constant term 5. This is a direct application of rational root test. The proof of the above test can be done using Euclid's Lemma or Gauss's Lemma. June 10th, 2011, 07:56 AM #4 Newbie   Joined: Jun 2011 Posts: 4 Thanks: 0 Re: Why can't 3/2 be a factor of this polynomial? I understand now, the rational root test gives all rational (hence the name) roots. This just hadn't clicked with me. Thanks for the replies! June 10th, 2011, 06:04 PM   #5
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 Originally Posted by figgy Why can't be a factor of ?
I assume you're asking why can't x - 3/2 be a factor of the polynomial? Because 3/2 is clearly can be a factor of the polynomial. June 12th, 2011, 06:31 AM #6 Newbie   Joined: Jun 2011 Posts: 4 Thanks: 0 Re: Why can't 3/2 be a factor of this polynomial? I actually wanted to know why 3/2 couldn't be a root of that polynomial, I just asked the question wrong. Tags 3 or 2, factor, polynomial Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Mr Davis 97 Algebra 1 March 2nd, 2014 08:15 AM shiseonji Algebra 3 August 4th, 2013 12:12 PM mrmorris Algebra 5 August 30th, 2011 11:36 AM noname Abstract Algebra 2 November 17th, 2006 07:39 AM

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