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Synthetic Division
Example 1. The divisor is a monic (coeff. of highest power is 1) 
linear polynomial 
Divide 
: 
x  x  x  by x  
    4 3 
2 8 2 2 .
Divide 
: 
x  x  x  by x  
    4 3 
2 8 2 2 .
Example 2. The divisor is a linear (not monic) polynomial 
Divide 
: 
x  x  x  by x  
    4 3 2 
8 12 6 1 2 1 .
Divide 
: 
x  x  x  by x  
    4 3 2 
8 12 6 1 2 1 .
Example 3. The divisor is a monic quadratic polynomial 
Divide 
: 
x  x  x  x  by x  x  
    4 3 2 2 
3 2 9 8 2 .
Divide 
: 
x  x  x  x  by x  x  
    4 3 2 2 
3 2 9 8 2 .
• http://www.qc.edu.hk/math/Certificate%20Le 
vel/division.htm

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Lecture synthetic division

  • 2. Example 1. The divisor is a monic (coeff. of highest power is 1) linear polynomial Divide : x  x  x  by x      4 3 2 8 2 2 .
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8. Divide : x  x  x  by x      4 3 2 8 2 2 .
  • 9.
  • 10. Example 2. The divisor is a linear (not monic) polynomial Divide : x  x  x  by x      4 3 2 8 12 6 1 2 1 .
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17. Divide : x  x  x  by x      4 3 2 8 12 6 1 2 1 .
  • 18. Example 3. The divisor is a monic quadratic polynomial Divide : x  x  x  x  by x  x      4 3 2 2 3 2 9 8 2 .
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25. Divide : x  x  x  x  by x  x      4 3 2 2 3 2 9 8 2 .
  • 26.
  • 27.
  • 28.