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Unformatted text preview: r there is another polynomial
Q(x), called the quotient, with degree one less than the degree of P(x) and a number R, called the
remainder, such that, P ( x) = ( x  r )Q ( x) + R
Note as well that Q(x) and R are unique, or in other words, there is only one Q(x) and R that will
work for a given P(x) and r.
So, with the one example we’ve done to this point we can see that, Q ( x ) = 5 x 2 + 19 x + 76 and R = 310 Now, let’s work a couple more synthetic division problems. © 2007 Paul Dawkins 247 http://tutorial.math.lamar.edu/terms.aspx College Algebra Example 3 Use synthetic division to do each of the following divisions.
(a) Divide 2 x 3  3 x  5 by x + 2 [Solution]
(b) Divide 4 x 4  10 x 2 + 1 by x  6 [Solution]
Solution
(a) Divide 2 x 3  3 x  5 by x + 2
Okay in this case we need to be a little careful here. We MUST divide by a term in the form
x  r in order for this to work and that minus sign is absolutely required. So, we’re first going to
need to write x + 2 as, x + 2 = x  ( 2 ) and in doing so we can see that r = 2 .
We can now do syn...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
 Spring '12
 MrVinh

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