The graphs of polynomials will always be nice smooth

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Unformatted text preview: verify that this fact is true for the polynomials listed there. This will be a nice fact in a couple of sections when we go into detail about finding all the zeroes of a polynomial. If we know an upper bound for the number of zeroes for a polynomial then we will know when we’ve found all of them and so we can stop looking. The next fact is also very useful at times. The Factor Theorem For the polynomial P ( x ) , 1. If r is a zero of P ( x ) then x - r will be a factor of P ( x ) . 2. If x - r is a factor of P ( x ) then r will be a zero of P ( x ) . Again, if we go back to the previous example we can see that this is verified with the polynomials listed there. © 2007 Paul Dawkins 252 http://tutorial.math.lamar.edu/terms.aspx College Algebra The factor theorem leads to the following fact. Fact 1 If P ( x ) is a polynomial of degree n and r is a zero of P ( x ) then P ( x ) can be written in the following form. P ( x) = ( x - r )Q ( x) where Q ( x ) is a polynomial with degree n - 1 . Q ( x )...
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