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Unformatted text preview: uick example to remind us how long division of polynomials works. Example 1 Divide 5 x3  x 2 + 6 by x  4 .
Solution
Let’s first get the problem set up. x  4 5 x3  x 2 + 0 x + 6
Recall that we need to have the terms written down with the exponents in decreasing order and to
make sure we don’t make any mistakes we add in any missing terms with a zero coefficient.
Now we ask ourselves what we need to multiply x  4 to get the first term in first polynomial. In
this case that is 5 x 2 . So multiply x  4 by 5 x 2 and subtract the results from the first
polynomial. 5x2
x  4 5 x3  x 2 + 0 x + 6
 ( 5 x 3  20 x 2 )
19 x 2 + 0 x + 6
The new polynomial is called the remainder. We continue the process until the degree of the
remainder is less than the degree of the divisor, which is x  4 in this case. So, we need to
continue until the degree of the remainder is less than 1.
Recall that the degree of a polynomial is the highest exponent in the polynomial. Also, recall
that a constant is thought of as a pol...
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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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