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"5.4 Synthetic Division
供稿人: Smith
Only the numbers are used, no variables
           Synthetic Division is
dividing a polynomial by a binomial
(2x2 -1x-3) ÷ (x+1)
(2x2-1x-3) ÷ (x+1)
The x value
that cancels
the divisor (-1)
is the multiplier
The answer
(quotient):
   2x - 3
(2x2-1x-3) ÷ (x+1)
x
#
remainder
The
quotient
is:
(3x3+5x2-2x-120) ÷ (x-3)
 3x3+14x2+40x
 3x2+14x+40
The
quotient

(3x3+5x2-2x-120) ÷ (x-3)
x2
x
 3x2+14x+40
#
remainder
Quotient:
(5x3-6x2+3x+14) ÷(x+1)
 5x2-11x+14
 5x3-11x2+14x
The degree (highest power) of the quotient
is ALWAYS one lower than the degree of the dividend
Quotient : 5x2-11x+14
(5x3-6x2+3x+14) ÷(x+1)
(x2 -3x -10)÷(x-5)
Fill in the
blanks
5
(x2 -3x -10)÷(x-5)
1
-3
-10
5
(x2 -3x -10)÷(x-5)
1
1
-3
-10
5
(x2 -3x -10)÷(x-5)
1
1
-3
5
-10
5
(x2 -3x -10)÷(x-5)
1
1
-3
5
2
-10
5
(x2 -3x -10)÷(x-5)
1
1
-3
5
2
-10
10
5
(x2 -3x -10)÷(x-5)
1
1
-3
5
2
-10
10
0
The quotient:
x2+2
x2+2x
x+2
(x3 -4x2 -17x  +60)÷(x+4)
Fill in the
  blanks
-4
(x3 -4x2 -17x  +60)÷(x+4)
1
-4
-17
60
-4
(x3 -4x2 -17x  +60)÷(x+4)
1
1
-4
-17
60
-4
(x3 -4x2 -17x  +60)÷(x+4)
1
1
-4
-4
-17
60
-4
(x3 -4x2 -17x  +60)÷(x+4)
1
1
-4
-4
-8
-17
60
-4
(x3 -4x2 -17x  +60)÷(x+4)
1
1
-4
-4
-8
-17
32
60
-4
(x3 -4x2 -17x  +60)÷(x+4)
1
1
-4
-4
-8
-17
15
32
60
-4
(x3 -4x2 -17x  +60)÷(x+4)
1
1
-4
-4
-8
-17
15
32
-60
60
-4
Quotient:
1
1
x3-8x2+15x
x2-8x+15
-4
-4
-8
-17
15
32
x2-8x
x2-8
-60
60
0
The End
The End
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