Alg_Complete

# So if we could factor higher degree polynomials we

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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.

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